If available go with the Premiere Inn County Hall.
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Adjacent to Jubilee Park where you’ll find the London Eye ( book now to cut down on cost and to see if you have any interest in taking it). Its quite the sight as sun sets which in December will be as early as 4pm. Rather enjoyable seeing Parliament and Elizabeth’s Tower with the Big Ben clock light up. Be forewarned there is still scaffolding around Elizabeths Tower. Covid slowed down the restoration project. The hotel is also close to Westminster Bridge and the Thames.
As its December besides the crafts and food stalls they’ll be Christmas oriented booths to investigate.
https://jubileemarket.co.uk/
Like acraven I’ve slept comfortably on the daybeds which are located as an addition to regular beds in Premiere Inn rooms. Also used them to lay out clothes and my luggage.
Both The County Hall and Victoria Premiere Inns are located near the sites most first time visitors want to see: Parliament, the Big Ben clock, Westminster Abbey, Buckingham Palace, Tower of London.
IMHO opinion the Changing of the Guard is a complete waste of time. Instead take the children to see the Horse Guards on their parade ground as they mount up to proceed along the Mall to the Palace. https://changing-guard.com/queens-life-guard.html
One note about Buckingham Palace, if the flag is up The Queen is in residence.
Their are numerous parks in London. If you stay at the County Hall Premiere and walk across Westminster Bridge to Parliament Square you can follow Birdcage Walk adjacent to St James Park up to the palace. Not sure with Covid if the daily feeding of park’s Pelicans still takes place.
Across the Road from the Palace is Green Park.
Kensington Palace is adjacent to Kensington Gardens and Hyde Park. Near Kensington Gardens there’s the Round Pond and Princess Diana’s Playground. If you stroll through Hyde Park be on the look out for the green parrots that reside there. https://www.google.com/amp/s/amp.theguardian.com/cities/2019/jun/06/the-great-green-expansion-how-ring-necked-parakeets-took-over-london
Depending on the ages of the 3 children Hamley’s toy store might be a must visit. I think using the tube, and riding up top a double decker bus would be of interest.
Lastly, during the day children are allowed in most pubs, as are dogs. You’ll find tasty soups, burgers, crisps, bangers and mash, fish and chips, and pot pies. Look at Pret a Mangers, Sainsburys, Tescos and Marke and Spencer’s for pre made sandwiches.
Been to London for Christmas more than once. Given how Covid has restricted travel through the world, residents and tourists alike will be out and about in large quantities. Don’t be discouraged. Embrace it. Its London, one if the world’s greatest cities! Online check Timeout London and The Londonist. Great information.
Safe travels