I will echo what others have said about London being pretty easy to find vegetarian food in. I am vegan and haven't had much of a problem.
As mentioned above the salads at Pret are pretty good as are the takeaway food at stores like Marks and Spencer or M&S as their food halls sometimes seems to be labeled. I also enjoyed some Egyptian street food at a place called Koshari Street near the National Gallery. It was pretty good altho their hot sauce was not as hot as I like it, lol (based on the vendor who sells koshari at my local farmer's market who uses his grandmother's secret hot sauce recipe.)
I also enjoy another chain called Le Pain Quotidien (the daily bread) which does have vegetarian and vegan selections daily. I've eaten in the one near Victoria Station.
I don't remember your whole travel plan and if you are going to stay in the UK the whole time, but if you are taking the Eurostar to Paris there are 2 M&S food halls in the St Pancras station so it's convenient to get food for the train trip.