I previously lived in this property and never locked myself out of my room so I never looked nor do I even know if I have a key for the bedroom door.

I also suspect inflation will drive continued migration to lower cost of living / lower tax states.  

In this case, you can use Rental Income from the units that you will not be living in and that income can count to help you qualify.FHA rates are going to be lower than conventional for you almost always, but FHA does have a 1.75% funding fee. 

I was thinking maybe Houston because my boyfriend lives there and I’m there a good portion of the year as is, but I’m open to any good market.

FHA 203k wont work unless youre going to live in the property as your primary.

I'm familiar with the Greenville area, having lived in North Carolina for a few years.

I ask because I hear single section 8 tenants like to have their bf/gf living in with them...Quote from @Rich N.: @Peter GoellerBecause they way Sec8 does it, is that their local Sec8 inspector is suppose to the know the market rate.So, let me clarify this. 

My mum currently lives there, she is 80 and not very well, but you would also become a tenant in common and as such if you had the time you could profit 100% from the transaction, as I need cash urgently and am willing to heavily discount the asset.I am wondering if there is a market out there where someone wants to get a foothold in the London market by buying my part of the property.

It can be done but it may take years to build up cash flow especially if you live in high cost area like CA.   

I live in a rural market and this type of issue with technology may not be as big a factor in urban areas.