Cheap Apartments To Rent In Birmingham For 1 Night . Find cheap or luxury self catering accommodation. In fact, you can pick up some budget digs for under £75 a night, a steal in the centre of birmingham. London Luxury Apartments Luxe Apartments Rentals from www.luxe-apartmentsrentals.com Start your free search for cheap apartments today. Featuring a bar and free wifi, 21 frederick street is set in the centre of birmingham, close to museum of the jewellery quarter, coffin works and arena birmingham. This is a small cottage on a quiet little street.