Looking to Rent - 1 or 2 bedroom flat
Must be close to Birkenhead Town area
400-700 per month

You won't need anything like the top end of that budget to rent something in Birkenhead.

Check out the usual suspects like Rightmove but £700 will see you in the best that East Float has to offer I would imagine and will certainly see you in somewhere in Hamilton Square with plenty of character and 2 decent sized bedrooms.

Lower end of your budget will see you 'slumming it' in Rock Ferry or North End if you want a 2 bed, I would imagine but I'm not up with prices out that way.