Need advice with what to do with work I've just had done from my builder

We're you provided with a minor works certificate for these works? Any registered electrician should provide you with paperwork. Unfortunately my builder doesn't actually vet this and there are people on here who are not registered with a competent persons scheme. If you are concerned with the work raise it with my builder as they are responsible for listing the tradespersons. From what your pictures show there are several non compliances.

From what I can see (and this severely limits my accuracy here, as I do not know the supporting electrical systems, supply etc AND providing we are looking at the finished article as far as the electricians work), from what I can see in the photos alone, the only non compliance with respect to the bs7671 is that there is no additional protection for the exposed cores' insulation, and if there is no RCD protection this provides serious danger and is unsafe (level c2 on an eicr). That's what the regs state, however the rest of the work 'may' be perfectly suitable for the next stage which is filling, and once filled would be safe, however those ends are not suitable for filling in that exposed state, the rest may (or may not) be fine. For the actual overall assessment of works (if) completed, this is utter rubbish, regs or no, and any fool that thinks leaving ends like that is ok for filling is not suitably competent. It's shoddily, dangerously installed, pursue having the charlatan who left it in this state removed from Mybuilder. All the best.

Looking at the picture cables joined together by twisting them. Then installation tape isn't a proper joint I take it you don't want a socket there . The best way is to use maintenance free connectors and put a blank plate on top but of you want to lose the socket altogether and there is access under the floor then again a maintenance free junction box would work or maintenance free connectors in an enclosure

The work doesn't comply to the wiring regulations and it is unsafe! You have to arrange a visit from a qualified electrician to check everything and rectify the work. An Electrical installation certificate shall be provided once the job is completed.