Both the Madid Barajas Airport website and the Birmingham International Airport website state that there are currently no direct scheduled flights from Madrid to Birmingham. The prices you've found are almost certainly for connecting flights, which are usually more expensive anyway.
Flights from Birmingham don't go anywhere near to Madrid. (The nearest airport, which is served directly from Birmingham, is Valencia but that's a very long train journey away).
The nearest airport to Birmingham, served directly from Madrid, is Manchester. The 1635 flight with Ryanair, on 13th May, is currently priced at €27.99. It lands at 1825. The 1929 rail departure from the airport will get you to Birmingham New Street at 2132. (Or the 2000 will get you there at 2200. Change at Manchester Piccadilly in both cases). The advance purchase fare is currently £17.00
There's a £17.00 advance rail fare currently offered on the 1401 service ex Birmingham New Street (arriving at 1617) or on the 1531 (arriving at 1729). Change at Manchester Piccadilly again. The return flight leaves at 1850, arriving in Madrid at 2240, costing €27.79.
http://www.ryanair.com/en
http://www.nationalrail.co.uk/
Chris