We found Thomsonfly do from Birmingham and East Midlands. Whether they do from Manchester I'm not sure, but worth a try. You need to go into the various airlines websites and check under cargo. Some list various pet agents and they do vary in price. We were quoted anything from £225 incl. up to £550!
www.ana-aviation.com might be able to help. But you cant currently book on line as they were making changes to website. We are using Whitely Sky Dogs based at Tamworth, they are not your area but might be able to help. tel 01629734000. By the way not all flights cater for animals, so you have to book cat on flight first then see if there are any passenger seats. We booked our cat on three times before we were able find seats on same flight! Good luck. Sylvie