Will sign up on my phone, So to clarify once signed up then i can use a vpn? Sorry I have no idea how vpn works, I don't wannt to end up paying for a vpn only to find out I cant use it.
Nobody can tell you what services the council has blocked, or how. We're not psychic. Many companies block entire VPN IP ranges these days (Netflix, Amazon, BBC etc), it's trivial. Do you have IPv6 connectivity or just IPv4? Your best bet is likely to sign up for a lesser known/smaller provider like Mullvad, AzireVPN, WireVPN or (insert small service here). They're less likely to be blocked outright, and in any case less likely to have their many endpoints on a blacklist even if their main website is. For the sake of a couple of quid for one month's service, you've not much to lose - especially as they predominantly offer a money back guarantee (you're pushing it there, as the problem's at your end, but they're decent companies and should be OK about it). Connect over mobile/public WiFi, make an account and get the configs, save them to your PC/laptop/whatever, and then try to connect via the Council WiFi.
Some protocols may be blocked but not others (eg they may block OpenVPN but not IPSEC, or WireGuard etc). Ditto some ports. Try something like WireGuard over port 443 or 53 if the defaults fail. Just experiment. Likely you'll soon be up and running as most services don't spend much money on trying to enforce really strict DPI, rather they rely on a firewall to funnel traffic to basic ports (53 for DNS, 80 for web, 443 for TLS). You can generally take advantage of that.