Webhosting.uk.net - who offer vps and dedicated servers in UK. I do not have any experience with their vps or dedicated servers, however I have been on their reseller plan since last few months now and must say their network and support is simply great. If they offer such a good support for their shared client base, I am sure, they will offer similar support for their vps and dedicated clients.
Talk to Craig over at www.Kualo.com , they have been in business for a good number of years, have a friendly rapport with their clients, and do a very good job to the best of my knowledge for their UK clients.
It sounds like you are having a software problem rather than a problem with your host.
Your providers firewall will likely be protecting mysql's port, keeping out foreign connections. If you ask them to remove all protection you should be able to access mysql freely, but you'll then have a potential security problem.
Mysql shuts off internet access by default, it binds to localhost. You probably do not want to connect to a mysql database without going over some kind of encrypted tunnel or you are asking for trouble.
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