My issue is that I can potentially pull out enough equity from the home to send my cash flows into negative territory.  

If it was me, so long as the tenants have been there for quite some time, they have record of regular payments, and a low tendency for trouble making, I would much rather take the paycheck than the negative cash flow  straight out of the gate. 

It's not in a great area and the opportunity for cash flow I am afraid will be negative for you every month.Say you rent it for $1500You subtract $1200 for mortgageThat leaves $300.Now you still have maintenance, insurance, and vacancy not yet in the calculation.10% is a good rule of thumb for those 3 things.That comes out to $450You lose $150 every month by holding this property.It doesn't sound like a great deal to me. 

There are bills that will come out of the woodwork for the most random things and with a marginal return, you will negative cash flow likely until it's paid off.

Though you're pocketing more than that, your interest deduction puts you at a negative tax liability.

If existing British owners rushed to sell, accepting prices under market value just to get out, this would have a negative impact on the market.

cap rate would be negative, still buying it?

@Allie Reeves if your in a negative cash flow scenario it's time to sell.

I  don't mean to be negative, I just want you to attain enough money to finish the deal with the least stress possible.Do you by chance own a home that you can have enough equity in that you can use a home equity line of credit (HELOC) that you can borrow from?  

My team and I have crunched a ton of data on the city, and it never made sense to me why people still buy NYC properties for investing; albeit you do benefit from price stability and perhaps even tax reasons given you'll be negative cash flow most of the time.