I purchased a 2013 Focus 1L Ecoboost 46k Miles FSH.

After 2 weeks the car went bang with the coolant problem which resulted in total engine failure, the car went back to the dealer in Birmingham I brought the car from who in turn took it to Ford who agreed to fit a new engine and components at no cost. The ford garage had my car 5 weeks, picked the car up on tuesday was told he needed to jump start as it had been sitting and didn't think anything of it as I stopped at a petrol station and it started first time.

I went to drive it last night for the first time and it would start unless jumped, no warning lights or indication. I took it too my garage this morning thinking it is the battery however after changing the battery it's exactly the same not starting unless jumped/bumped. Any idea if this sounds like a starter motor problem?

More likely an alternator problem...possibly a loose connection perhaps but it should be down to your Ford dealer to fix if the problem wasn't there before you had the new engine fitted ??

Take it back to the dealer who fitted the engine, they've missed a step somewhere