I use callcentric.com and have the same USA number we've had for over a decade. You can choose from various calling plans, and you can set it up to have the number forward automatically to your UK number. We have a pay-as-you-go plan, where I pay $2.95 a month for my US number and to use the service. If a call comes in, it immediately forwards to my UK number (or I can set it to voicemail, with an email notification option), or I can set it to ring a separate phone here. I'm charged literally a couple of pennies a minute, but there are plans where you pay bit more up front and there are no per-minute charges, I believe. I like the ability to download various usage and billing reports, and to block specific numbers. You can have several extensions on the one main phone number, as well. There is a user-friendly dashboard where you can set everything up.
I use my old USA landline handset here, connected to an adapter on my computer, to make calls on it as if I was in the States. (There are interfaces to use it on your computer/tablet, etc., but I prefer a handset with the American ring.) As noted above, I can also set calls to come directly to this phone, and they ring in the typical one-ring USA style so I know I've got a USA call coming in. (Useful if I'm waiting on an important call, but I usually have it sent to voicemail and just call people back, due to the time difference, after having gotten several 2:00am calls when I had it set to ring separately or forwarded to my UK number.)
They have only recently had SMS capability and I don't do text messages, so I'm not sure how that would work for you overseas, but I think there's an ap that you can put on your cell phone and you can send and receive them via that ap no matter where you are. They're pretty good about answering emails within a day, though, so you might check with them to see if they have something that would work for you.
https://www.callcentric.com/products/