Unfunded UK PhD offers - both deadlines imminent
I wouldn't recommend it. I started a PhD when I had my own funding for the first year. The second year some money was scraped together, but after that there was a complete failure to find funding. Things got ugly. 

If you are really intent with working with one of these two PIs, make sure they have a solid and extensive track record with funding. If these are new labs, forget it. But since you don't seem overly interested in working with them, I would say find a safer option.