The perfect world answer is no . You must contact your service provider who will arrange for a BT Openreach engineer to do the work at their outrageous hourly rate.
BUT in reality most service providers will tell you to get an electrician to do the work - but BT count this as trespass and it is illegal. However you can't contact BT Openreach directly as they wont talk to end users so back to your service provider you go. Who will tell you to contact BT Openreach ....etcetera etcetera etcetera .
BT do not keep a record of where your main socket is and would never visit your property unless you ask them to , so , if an electrician where to do the work for you , as long as he didn't mess it up and did it to the same quality standard as BT they would never know the difference and if any one asked which they wouldn't, " It was like that when I moved in guv ". The job is almost as easy as putting in an extra socket and requires no specific mandatory qualification unlike a gas fitter would legally be required to be Corgi registered to work on gas.
Is BT trespassing on your wiring when BT remove your face plate / extension wiring to test ?