Radial cable joined with strip connector and taped up under floor

Absolutely not! this is not compliant with BS7671:2008 and therefore the electrical certificate he issues at the end of the job (assuming he issues one!) is invalid. Depending on what room this has been done in, could also leave you open to a £5000 fine from building control. Sounds very much like you have hired a cowboy and not a Part P registered electrician?

No it is not. Electrical joints are a potential source of overheating and if not securely made could ultimately cause a fire. For this reason there are several regulations relating to electrical connections. Indeed this is mentioned within chapter 13 in regulation 134.1.4 ‘Every electrical joint and connection shall be of proper construction as regards conductance, insulation, mechanical strength and protection’ Regulation 526.3 requires that every connection shall be accessible for inspection, testing and maintenance. There are 6 exceptions to this rule. Exception (vi) is: “Equipment complying with BS 5733 for a maintenance free accessory and marked with the symbol and installed in accordance with the manufacturer’s instructions”. So no, he has broken a number of regulations and the joint should be done properly with the right equipment. Problem is that doing it properly costs more and the cowboys get more business by undercutting. You have employed a good old cowboy who probably doesn't know any better.