It might be the laptop releasing its IP address and renewing it at the same time every night. See if other devices lost connection too and if not, the problems on the laptop side.
If they are all doing it, it might be the router renewing its address every night so log into the router if you can and have a look in the settings.
If your in doubt, call Talk Talk and offer these suggestions if its still happening. They should be able to talk you through it.
Hopefully related to this thread, I read in the paper today that they are going to do away with all landlines on the grounds that they are ‘old fashioned’ and that most people now use mobile phones.
It appears that the only options for telephones will be mobile phones or phones using the internet, such as VOIP. The article pointed out that this will impact on older people especially who don’t have broadband or mobile phones.
Well, it was the Daily Express!
Art, this might not be related in any way, but I remember a few years ago my telephone would make a sound, it wasn’t even a ringing…but it was at the same time every night, about 10 45pm…when I lifted the receiver…the line was dead…when I finally managed to contact BT they told me that they checked the line at that time every night…they sent someone out to check it and found nothing wrong…this went on for ages until they sent one guy out and he said he wouldn’t stop till he found the problem…it took him all day but he did find that it was a fault at the exchange a couple of miles away, he fixed it , no problem since…this was only my phone line…I didn’t have a computer then. but as your problem seems to be at the same time every night, it might be something similar, hope you get it fixed soon
Reading this thread it doesn’t appear the problem has been solved. A neighbour of mine had something similar happen every night at the same time, I think that was about 21.15 hrs. He was into technology so checked and double-checked but could find nothing. Then one evening he was just looking out of the window when his internet went off, as usual, at the next evening the same but he noticed one common factor in this – the street lamp right outside the house would come on just as the internet dropped out! He contacted his ISP and a BT engineer checked this out and it was that street lamp causing his internet connection to drop out. A small ‘box of tricks’, a type of filter, fitted to where the overhead telephone line came into the house, before the BT main socket, cured the problem.
Apparently there are many things that can cause this kind of problem, anything outside like a Belisha beacon, traffic lights etc. It’s perhaps something to do with, and I am guessing, the magnetic field that is set up. Indoors, microwaves and other devices can cause problems with wifi, it’s all too clever so it’s even easier for it to go wrong I reckon. 
