I sympathise with what you are trying to achieve here, i.e. having your cake (no VAT on selling bitcoins) and eating it too (recovering VAT on mining equipment) - BTW I am not an Englishman so I am allowed to use stale expressions ;-)

But it is not that simple - the general rule remains that you cannot recover input VAT that relates to exempt output. Here, you are buying an ASIC, an "Application-Specific Integrated Circuit" that can only be used for making an exempt transaction, i.e. selling bitcoins.

Basically put, you only have a shot at recovering the VAT on the ASIC if your selling bitcoins is only marginal compared to your other, non-exempt, activities (i.e. you have a lot of input VAT you can recover). See the "de minimis rule" http://customs.hmrc.gov.uk/channelsPortalWebApp/channelsPortalWebApp.portal?_nfpb=true&_pageLabel=pageVAT_ShowContent&propertyType=document&id=HMCE_CL_000857#P42_4728 .

The non-exempt activities could be anything: consulting, transaction fees, etc etc. If you have another business that is registered for VAT and not exempt, you could also try to meet the thresholds together as a VAT group.

You should check all of the above with a good UK accountant or tax specialist but if the VAT system in the UK works more or less like it does in the rest of the EU, here's your answer.