Bridle path/way

Is it legal to drive a car on a bridleway ?

Only with the landowners permission apparently. Not something I've ever had to worry about.

If it's just designated as a bridleway, I beleive it's an offence to use a motor vehicle on it. However, there is still the odd track that's commonly referred to as a bridleway that is actually considered to be a "green lane". Such green lanes are now designated as Byways Open To All Traffic (BOATs). Provided that there's no further Traffic Regulation Order (TRO) applied to them, it's legal to use a properly licensed, taxed and insured vehicle on them. The difficult bit for the genuine off road enthusiast is identifying such byways.

Most Police websites have guidance on what's legal or not. Naturally, the more rural ones tend to go into greater detail.