I paid a similar price recently also booked at last minute. I've just returned to Australia from a holiday in Europe. On my travel agents advice I decided to leave UK by taking Eurostar from London to Paris. Incidentally I arrived in London via Amsterdam.
The Eurostar trip itself was pretty pleasant booking it on the otherhand not so much.
I should have purchased the tickets well in advance before leaving Australia instead I left it until the last minute - I blame bad advice from my agent who basically told me. "Oh you can just rock up to train station on the day purchase a ticket to Paris, no big deal".
In Amsterdam I was advised that I may not be allowed into the UK unless I could show them I had a departure booked. So I had to buy the Eurostar ticket in a rush. Eurostar website did something weird with my credit card tripped up some sort of Fraud detection or something Triggered 2FA check with my Australian bank. Bank's text message went to my Australian SIM which of course was inaccessible from Amsterdam. I'd used this credit card all over Europe for 5 weeks up until this point with 0 issues I have no idea what it was about Eurostar site that triped their fraud detection. I had a backup prepaid Visa debit card which the Eurostar site also refused to accept. I ended up ringing friend of mine who lives in Rome in a panic and he was able to order tickets for me.
Border Control did ask how I was planing on leaving the UK I told them Eurostar and they waved me through without asking to see the physical ticket.