we are traveling in april, can we book the train from london to paris in london
Yes, but it will be very expensive. Try to book it as soon as possible (but no more than 120 days ahead). You can book it now and save some money.
Robert - Although you may well be able to book from London, I would buy my tickets in advance unless you have no idea what date you are making the crossing. I just bought our Eurostar from Paris to London today - our trip is in June - and this is the first day the tickets are for sale. I paid $72 per person. But as I was researching dates over the last few months, I noticed that the prices increase exponentially as the dates get closer. I noticed today that some of the trains in April are $139 per person for the same departure I bought for $72 today.