First, your gf is a UK citizen moving to another city within UK? She has no problems. She just needs to find a job in Ipswich first, then find an apartment.
As for you, as a Swedish citizen, what's your status in UK and do you have legal authorization to reside & work in UK without restriction. Of course, if you are on employment visa, you can ONLY work for the employer which obtained your employment visa. If you have unrestricted rights to live & work in UK, then you also need to find a job in Ipswich. Then you have the appropriate documentation to meet landlord requirements to rent an apartment/flat.
There is no way around this. Find suitable jobs so that you can afford rent, utilities, all your living expenses, or you cannot get a lease on a place to live!