A plea for advice

I intend to start applying for mortgage in next 4 months and as part of the planning process requested to check my credit report via equifax to my amazement my score was 368 ( just fair) . I also had a recent late payment showing last month on my Lloyds CC, and 2 other late payments one in march 2012 and the other November 2011
This cards are all up to date.
Can I ever get a mortgage with this circumstances, am on 43k and partner is on 47k annually and we are looking 15% mortgage

Partner just moved to Uk in November so no credit rating has been built in real sense.

Please I really need any advice