So, the engineer came out yesterday and seemingly has fixed my problem.
The REIN engineer arrived around 1pm. Although I had mentioned to BT that the problem didn't start until between 3.45 and 4.30, the guy said he had seen a little interruption here and there throughout the day and thought he'd come and have a look. As there was nothing going on, I made him a cup of coffee and we sat around waiting for something to start. After reading information online about the stringent time restraints and stuff, I was relieved to have a guy around who seemed happy to wait.
He was performing ongoing checks and at 3.45 the internet went haywire. He started to check for REIN and couldn't find any. He traced the line to the small box at the rear of the house and found that the issue was being caused by interference from someone else's broadband line. Somebody was coming in, switching their router on (at the wall by the looks of it) and it was causing me to disconnect.
He changed a few wires around and it ran smoothly aside from a couple of disconnects.
What is strange, is that without a shadow of a doubt when my internet crashed I could hear a huge change in the noise through my radio at 612khz. I was quite surprised it was nothing to do with any REIN interference.
Either way I'm glad to have the issue sorted.
Once again that's for all the advice on here. It was much appreciated.