I can say this with a fair degree of certainty - as a UK resident (and assuming your business is registered in the UK) you will be liable for taxes in the UK only. In addition, a web based service would most likely be seen as 'electronically supplied services' by HMRC and generally speaking, supply of such services to an EU business is typically 'out of scope' of UK and EU VAT, so does not count towards the turnover level you need to meet to become VAT registered, nor would it be eligible for VAT should you already be VAT registered.
Server location means nothing with regard to taxes.
As usual though, consult an accountant who understands these things - many have no idea about the VAT loopholes relating to electronically supplied services. I would also assume that, as a 'service provider', you'd be better off running this through a limited company to give your assets some protection should anything go 'wrong'.
BTW, HMRC can also advise on the VAT and tax issues, and you can request that their advice be sent to you in writing, which could be useful should you ever have any problems with them in the future.
I sell digital goods mostly to the US, and got written confirmation that those transactions were out of scope of VAT.