After years of messing about with 'cheap' PAYG US-based phones, and wasting time and $$, and because I don't actually use my cell all that much anyway, I decided on a PAYG with 3. On the last trip, it was great. Called DH, he called me, no problems.
As I am retired, I don't have a work issue, and my father's land line sufficed for local calls.
I recommend 3 for the calls to the UK part. Actually, I've been much happier with coverage etc. with 3 over O2. I get a signal when some other family members on other carriers don't. Definitely worked for me.
I've used Vonage back when I worked, and the call forwarding sounds like a decent way to go. Alternatively, just get a cheap disposable (Net10 or similar) on the cheapest sim available, and give non-business contacts the *new* number.