Part and part. Osborne promised a punishment budget immediately after the vote. The CBI said the UK economy would collapse, before leaving the EU.
JLR was already in the works and has been facilitated under EU conditions. Essentially the world slowdown has hit extremely expensive JLR vehicles so they are moving them to cheaper manufacturing in Eastern Europe. This would have happened whether or not Brexit had been called. As for Dyson? They use the UK for R&D, China for manufacturing and moving the HQ to Singapore wont change that much after the EU tantrum over Apple earnings domiciled in Ireland for sales in other countries.
As for the long term impact of Brexit? Back office moves will not tell us much. HQ moves and business residency is much more of an indication and that is still as unclear as the solution to Brexit.
I agree, thought, that May is now the problem. They need to fix that first.
The Leave campaign may have banged on, constantly, about immigration. But they also talked about job stripping, industry stripping, sovereignty and a host of other issues. It was the press who constantly only repeated the Immigration issue. There were a host of issues including money and respect. The only part of money that got air time was 350, respect got absolutely none. Nobody I talked to about it had Immigration as their #1 issue. An additional issue, yes, core? No.