"Seals! Over there!" my daughter breathes, pointing excitedly along the beach – apparently at a shoreline sweep of black rocks.

Except as we edge closer, I realise she is right. Occasionally one of the prone lumps rises and drags itself over the sand towards the water.

A deep sea smell – part animal, part harbour – drifts towards us and there's a low, honking kind of singing from the hundreds upon hundreds of Atlantic grey seals lolling between the groynes on Horsey Gap beach in east Norfolk.

SEAL WATCHING ONLY IN WINTER

Here on a weekend break, we have come across a piece of magic that only happens in the colder months. Between October and February, the seals – which spend two-thirds of their lives at sea in the North Atlantic and can dive 70 metres beneath the surface – haul themselves ashore to calf their pups.

For three weeks, the vulnerable newborns – whose white fur is not even waterproof – are fed milk six times a day by their mothers – so they pile on around 2kg of weight daily, before being abandoned to fend for themselves.

Retreating to the grassy sandbank to avoid disturbing the seals – the signs say to stay at least 10m away – my kids, Eve, seven, and her big brother Max, 16, are torn between wonder at these powerful sea creatures, and horror at their callous parenting style. Their dad, Mark, and I semi-joke that abandonment is sometimes tempting for humans too.

The truth is all four of us had needed a break from the stresses of work, school and urban life, and while Norfolk – with its sweeping beaches – is well known as a summer destination, we couldn't wait that long to get away.

ARRIVING IN THE DARK

And so, on a chilly Friday evening, we found ourselves travelling in pitch darkness to Fielding Cottage, 20 minutes' drive west from Norwich and three minutes away from the little village of Honingham. The final part of the drive, down a narrow country lane, involves following directions to round a sharp right-hand bend, before finding the entrance "on your left immediately after the green barn". (Satnav, we've been warned, doesn't always work here.)

Warmth, modern and bright furnishings and comfy beds are our first impressions of our two-bedroom bolthole. Named Kingfisher, it's one of three adjoining cottages built 18 months ago in the style of traditional black wooden barns.

By 6am on the Saturday, long before dawn or the others wake, Eve and I are up, out and exploring in our pyjamas, jumpers and wellies. At the end of our little row, we discover a well-heated, open-all-hours games room, offering board games, books and table tennis.

As daylight breaks, we discover a large, fenced grassy area, accessed from the patio doors of each cottage, meaning younger children can also be safely packed off outdoors to play in freedom.

MEETING THE GOATS

Later, Sam Steggles, 38, the energetic farmer/entrepreneur who owns Fielding Cottage, pops by and offers to introduce Eve to the farm's eight female Boer goats. They normally live in a paddock but are wintering in a shed (with an old Christmas tree in the corner to nibble on).

Slightly nervous of the goats' curved horns, my girl climbs into their pen while Sam reassures her they are gentle and won't bite, especially as they only have bottom teeth. Crouching down and holding out a handful of food pellets in her palm, Eve lets the inquisitive animals approach.

Sam also allows us to poke our heads round the door of his pristine factory, where he starts work at 1am on Mondays and Wednesdays to produce around 50 tons of Fielding Cottage cheese each year, in a giant metal bath stirred by two huge paddles. The milk to make it, he explains, is now brought into the farm, and the little herd we have just met, are kept as pets.

There's clearly plenty of hard work to be done in Norfolk but, for our family, this weekend offers freedom and a chance to slow down beneath vast grey, wintry skies.

DISCOVERING A SITE OF SPECIAL SCIENTIFIC INTEREST

We spend the rest of our Saturday morning at Horsey Gap, wandering southwards as we gaze at the seals, before finally crossing to the other side of the dunes. We find ourselves on a gorgeous part of the 84-mile long Norfolk Coastal Path – Winterton-Horsey Dunes, a 427-hectare Site of Special Scientific Interest.

Come springtime, little tern birds will nest on the beach and rare natterjack toads will breed in shallow pools. But on this chilly day (it's around 6C) the grazing marshes and leafless birch woodland are still, quiet and starkly beautiful, and it feels liberating just to breathe.

Exploring historic Norwich

Dusk approaching, we drive to Norwich, and venture into the city's 900-year-old Norman Cathedral as the choir is singing (entry free, recommended donation £5 per adult, £12 per family group).

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Strolling through the spectacular medieval cloisters, we nosy up a narrow spiral staircase to find a treasury filled with 16th century golden cups and plates that the local parishes "forgot" to melt down in the Reformation. Norfolk, we suspect, has probably always done things its own way.

Next we explore Elm Hill, a cobbled lane flanked by Tudor buildings, and delight in the antiques and collectables on offer in a converted church Saint Gregory's Centre for the Arts, finding a £28 rotary phone, old royal wedding thimbles for 50p and Beano magazines from the 1980s.

EATING AT AN UNUSUAL FISH AND CHIP SHOP

Hungry after all our exploring, we drop into the nearby Grosvenor Fish Bar, expecting plain fish and chips for supper. That is on offer (haddock £7, regular chips £2) but there are surprises too – Max orders The Krusty Krab Po'boy (£9.50) and is startled to find a whole soft shell crab inside his roll.

The seating area downstairs turns out to be in an underground grotto and, had we wanted alcohol, the chippy was happy to deliver our food to The Birdcage pub across the road.

CYCLING AROUND BLICKLING ESTATE

On Sunday, we set off for the National Trust-run Blickling Estate, 18 miles from Fielding Cottage, fully intending to explore 15th century Blickling Hall where Anne Boleyn was born.

But the day is too bright to be indoors, and we veer off course again when we spot the cycle hire (adults £5, child £4 for three hours).

Max and Mark tear off ahead on the four-mile trail, while Eve and I pedal more slowly and find a few short cuts. Our rides take us past open fields and through the centuries-old Great Wood (it might have been there since the first trees started to grow after the Ice Age, according to the National Trust).

We crunch over beech seed husks in places, avoid tree roots in others and stop frequently to admire incredible views of the Hall, its grounds and lake through the bare tree branches.

Blood pumping, none of us feel cold until we stop pedalling. Then we realise it's almost freezing and it's time for a hot chocolate in the cafe.

HOW TO PLAN YOUR TRIP

Fielding Cottage (fieldingcottagenorfolkholidays.co.uk; 01603 880 685) near Honingham, Norwich has three holiday homes: Kingfisher and Nightingale, which each sleep up to four people, and The Nest, which sleeps two.

Kingfisher and Nightingale each cost £125 per night (min of three nights) or £110 per night (min of seven nights). The Nest costs £90 per night (min of three nights) or £85 per night (min of seven nights).

Cheese-making courses at Fielding Cottage can be booked online, costing £80 per person. The next dates are May 15 and May 16.

For more information on places to see and visit in Norwich, go to Visit Norwich visitnorwich.co.uk or call 01603 213999.