I think Deli West One are opening a larger branch soon on the same street.
The John Lewis food hall on the basement (Oxford St) sells KLBD challah and rye bread - you have to go to the bread section in the far left corner. The other corner has a small selection of kosher dry goods.
Selfridges has a good selection of kosher - Adafina sandwiches and deli counter plus a dry goods shelf too.
Many products are supervised by the KLBD but don't necessarily have a visible hechsher - you need to check their website.
DD's sandwiches quite widely available in Central London - check their website.
Otherwise Rubens and Bevis Marks (City) best bets for Central London although only BM is open Motzi Shabbat in the winter.
Otherwise get tube up to GG/Hendon/Edgware.
I can't comment on Shabbat but I was in HK for 3-4 days during honeymoon in 2010.
I ate at all the kosher places and thought Mul Yam was excellent - albeit we were the virtually the only people in there (a midweek at about 7pm) and the service was pretty cruddy.
The JCC meaty restaurant was good, albeit a little pricey - but it was pretty busy so at least a bit of an atmosphere. Make sure you book ahead as security is very tight.
I also ate at Shalom Grill which is attached to Shuva Israel on Connaught Road. Food was not very good, more of an Israeli backpacker place - but on Shabbat I'm sure it will be fine as there will be services at SI within the same building.
You can also eat with Chabad, I'm sure you wouldn't go hungry
The Pillar hotel in Hendon is a kosher hotel (Federation hechsher) which should serve over Shabbat. Otherwise one of the hotels in GG (King Solomon, Croft Court etc) will do
Failing that, get Hermolis to deliver to your hotel - albeit you'll likely need to sort out how to keep the food warm.
Note that Bevis Marks Restaurant has moved - it's no longer within the synagogue complex - it has moved to bigger premises on Middlesex Street - about a 2 minute walk away from the shul.
Try this link:
La Fiesta is the only proper restaurant on there.
In recent years, Dizengoff in Golders Green has been open for Pesach (Sephardi Kashrut Authority). It may be too this year.
I believe Let's Meat is also open this yr during Pesach (SKA too) - but this is in Borehamwood so on the very northern outskirts on London - you'd need to get a train from Kings Cross to reach it.
Otherwise we don't have a great selection open during Pesach. There are only a few kosher restaurants in Central London, and they are never open during Pesach.
I'm from London - the certification for DD's is 100% valid - KLBD & Kedassia so no problems there.
The sandwiches are very good and can be found pretty easily over most of Central London. I believe DD's are owned by Hermolis (they are based in the same factory) so quality is assured.
Any other recommendations just ask.
In terms of Central London restaurants, you're restricted to Reubens (Sephardi Kashrut) in Baker St and Bevis Marks (Sephardi Kashrut) in the City - although there is due to be a new restaurant opening down the road from Reubens soon - KLBD.
Otherwise hop on the tube to Golders Green/Hendon/Edgware.
Hope that helps