TL:DR; Yes, the UK has potential wind resource to power itself many many times over. Yes, it could be five times as much (range: 4-200x). No, its technical potential harnessable wind resource is not 2000 TWh a year - it's much larger, but we don't know how much more; it's probably in the range 10,000 - 80,000 TWh/y.
For context, UK primary energy demand is of the order of 2500 TWh/y (Digest of UK Energy Statistics 2013, p14); final energy consumption is about 1630 TWh/y (ibid); electricity is currently around 376 TWh/y (ibid p113). So it depends which of those figures you take, and which of the estimates you use: the potential wind resource is somewhere between four and 200 times the size needed to power the country.
How much larger the potential wind resource is very unclear, because there's an enormous potential resource, but we don't know how much of it is technically accessible. There are several reasons for this.
we don't know how densely we can site floating turbines - they only exist as prototypes at the moment.
we don't know how deep the waters are that we can harvest wind in. Although much of the UK's Exclusive Economic Zone is in waters of less than 700 metres depth, there are extremely strong winds in deeper waters.
we don't know how big the inter-array wake losses are if deployment ever got to saturation density. (see the discussion in the section "The modelling methodology smackdown" in my answer here) Given the scale of the potential resource, we won't get to within 20% of saturation density for many decades.
Here's one estimate of the UK offshore wind potential, which estimates it at 2.2 TW of mean electrical output: with 8760 hours in the year, that's 20,000 TWh per year - more than ten times the number you've found. (graph is GW mean power - multiply by 8.76 to get the equivalent TWh/y for non-leap years). You might want to deduct 10% for shipping lanes, but that's just a guess at what the right % would be.
Stuart Gatley's M.Eng ("An investigation of the potential of offshore wind power in the UK, University of Nottingham, 2012) estimates the offshore resource as being in the range 10,862-79,978 TWh/y (p56)
That's the offshore resource, which dwarfs the onshore resource. "The UK onshore wind energy resource", ETSU R-99, F Brocklehurst, 1997, estimates the technical potential in the range 20-50GW mean power - that's 175 - 438 TWh/y. (that number is from memory: I don't have the report to hand; I'll verify that on Monday; but safe to say it gets lost in the rounding of the offshore wind resource)