Last full tube on a Sunday is 2315... I've missed it loads of times due to late arriving BA flights on Sunday nights. 2351 tube only goes as far as Acton Town.
In situations like this I have often taken a taxi home and then called up customer relations the next morning and explained my problem, circumstances etc. It will cost around £50 to Westminster bridge area. They've covered my full fare a few times and partial fare other times.
In other situations BA have allowed me to travel on the next flight of the day and stay the night at my own expense.
Whatever option is best for you, or whatever works for you, I hope you get home safe and without too much hassle