I have a webhosting account in the UK (Linux)
Is it possible to install some sort of a web app that will allow me to use Windows VPN client to connect and use my server's IP address as a VPN server?
Take a look at logmein.com's hamachi vpn solution, it might be more easy to get going than an installation of OpenVPN (however I will say, if you're allowed to install apps, OpenVPN is not hard to get configured and running, probably a 4 hours learning curve to have something going if you're reasonably proficient with everything).
However if you just have a web hosting account, then there's virtually no way they are going to allow you access to the file system (this would be a gross security violation since most web hosting configurations are shared by multiple clients).
In any case, if you want VPN, you'll have to have access to the server, not just a web container on a shared server.
If you just want file access then use an FTP client, you can also use windows explorer to access an FTP site by adding it as a network place, then it just acts like an attached drive.
OpenVPN comes to mind, though I have no idea what you mean by "installing some sort of webapp." If you are on shared hosting you will not be able to do this in all likelihood. If you have a VPS this shouldn't be a problem.