Most baths are 170cm x 70cm
To get it to fit into the room most plumbers cut out a small section of plaster to let the bath fit in. Then when the bath is in and level fill the hole with plaster or tile adhisive.
I've just bought a Twyford Shallow for my ex-council bungalow with a small bathroom. It is 1500mm long, but may be too shallow for your needs. It may also be outside your budget at Â£320 inc vat (ish). There are some good web-sites offering short baths, but they seem to all come at a premium.