Like other British political parties, the Conservative and Unionist Party publish (and update) party rules, in their case branded as a Constitution. Any attempt to influence the party direction from inside the party would have to ensure it followed the rules described there, or else your insurgents would be told they weren't following the values of the Conservative party and asked (i.e. told) to leave. Similarly you would need to ensure that these new members hadn't broken any of the other rules, e.g. by maintaining membership of another party at the same time.
However, this document does also provide a template for what you need to do to take over: get control of enough local constituency associations to get your chosen people elected onto the National Conservative Convention. At this point, you're in a position to rewrite the Constitution as you see fit. This does mean you need wide geographic support for your movement.
Note that while this would win you control of the wider party, individual MPs are precisely that, individuals. They would be free to decide to start a new political party (the "Tory party", for example) and provided Theresa May maintained the backing of the majority of current MPs, she would remain Prime Minister.