REIN affecting my internet connection - please help?

I live on the 4th floor, which is the top floor, flat of which there is a lift.
When i moved in a year ago i was initially with talk talk and the internet was fine, every now and then it went pretty slow and maybe cut out once or twice a month. Ive now moved over to sky broadband and every day the internet cuts out.
Cut a long story short, the 4th engineer out of which was a bt engineer found that the lift in my block was causing REIN when ever it was in use and cutting out my internet/broadband. He had been to this block in the past a while ago and the customer noticed each time the lift went his internet went down so he tested if it was that and each time the lift went the readings went crazy and the connection then cut.
It sounds like this might be a long fix judging by what sky and bt have said.
Does anyone have any advice or expertise that may help me in getting this sorted quickly or any sort of fix i can do or device that will help prevent this affecting my broadband? it seems its the only the internet that is affected and no one else in my block seems to have had any problems... I reported it my landlord who said they will see what they can do but i was the first to report it...its driving me crazy.
And before anyone suggests, i have already thought about causing the lift to be 'out of use'....

So the lift motor is housed at the top of the shaft near your flat ? There may well be a line in the motor rom which might be picking up the interference and bringing it in close proximity to your line.
If so I'd suggest RFI filters fitted to both lines near the motor room, maybe a floor DP ?
Other than this, Openreach have no authority to do do anything at all, so you you'll have to get your landlord to get something done by the flats owners/maintainers.