Is it common to delay the start date of a postdoc?
It is very common to negotiate the start date. All of the postdoctoral researchers I hired or was involved in recruiting came at different times than advertised. Most funding bodies allow you to defer funding for a few months. For instance, EPSRC allows up to 3 months delay for start of projects. Also, most funders allow a so-called no-cost extension, meaning you can extend the end of the project without losing the money.

Just apply and in your cover letter say that you would be available in October, for instance.

Source: I am faculty (engineering) at a UK university and have been involved in recruiting 5 postdoctoral researchers.