If I invent something in my own time, does my employer have a claim on its ownership?

An invention made in your own time would normally belong to you. The law, whereby generally, an invention made during the course of an employee's normal duties, or in the course of duties specifically assigned, belongs to the employer, still applies.

Unless it could be shown that, in your own time, you were undertaking your normal duties or duties specifically assigned to you, the invention would belong to you.