I don't know enough to be able to identify the model, but a convertible Morris Minor 5142BY was integral to the BBC Play for Today, Nuts in May -
http://www.screenonline.org.uk/tv/id/548293/index.html

The entire play is on YouTube in 6 parts and the Minor is visible from the start, here -
http://www.youtube.com/watch?v=7CQYj_hDG7k&list=PL61647E6D04514896&index=106&feature=- plpp_video

It's an early (1957-62) Morris Minor 1000 Convertible. Rather a nice one.

Thanks Chris

Added to the TV Series 'Play for today' since Nuts in May is episode 12 of season 6. http://www.imdb.com/title/tt0074988/ http://www.imdb.com/title/tt0165592/episodes?year=1976

User is who should capture the pictures. I see this is your first contribution and I've done it for you but, next time, you should do it by yourself.

From other part, I see you are not member of IMCDB since your nick name is black on the TV Series page http://www.imcdb.org/movie_165592-Play-for-today.html If you think you are going to be member of IMCDB, please use the same nick as here on the forum, that is, Daytona.
Thanks.