If I fly through London, arriving on American, and on to Prague on British Air and it is booked all together

1. will I have to retrieve my bags and go through customs in London and

2. if so, what is the minimum recommended time to allow for this layover? One flight option just gives me an hour in London, another 5.

If I fly through London Heathrow, arriving on American, and on to Prague on British Air and it is booked all together.

1. Will I have to retrieve my bags and go through customs in London?

2. If so, what is the minimum recommended time to allow for this layover?

One of the possible flight options just gives me an hour in London, while another gives 5 hours.