You're probably looking for Send Anywhere (File Transfer), which is available (according to their description) for Android, iOS, and "PC". As the name suggests, this is not just for sharing files between devices you own, but you can share them with anyone using the app:
- Hit "Send" (generates a "6-digit one time key (OTK)")
- Give the key to the receiving party (or yourself ;)
- enter the key on the receiving end.
Now let's see how it meets your requirements:
- all be one program: no cross-compiled binary I guess; but yes, the same product on all devices.
- run on Windows 7, Android 4.0+, iOS 7+: Yupp.
- be under £20 altogether, no subscriptions: £0 should be OK? No signup or login required to me implies it should be free to use as well.
- be easy and simple: Admitted, the OTK is an "extra step". But apart from that, it sounds "easy and simple", right?
- be reliable: I cannot argue from own experiences, so let me quote from a market comment:
It does what it promises. It's a very efficient app. I have an ipad and a Galaxy s5 phone and always faced challenges tranfering stuff from one to the other. The easiest way was emailing, until a found Send anywhere. I gave it a 4 stars rating because it crashes once in a while, but I think that it's just when I try to transfer too many files at once. Anyway, it's definitely worth.
And it's the only one I'm aware of working on all the required platforms, apart from that. Some other candidates to check (I've not verified other than availability for Android, so I might have missed one) can be found in my app listing on Filetransfer between two Android devices.