These prices are a lot closer. You can play around with the assumptions in the government's LCOE calculator spreadsheet linked from the article. Removing the carbon price and using pre-wind load factor of 75% gives a LCOE of £67/MWh, which is similar in cost to solar at £65/MWh and onshore wind at £72/MWh, albeit lower than offshore wind at £91/MWh.
Assuming future costs of gas will go down is risky too. UK North Sea production is falling and recovery costs are likely to increase as we are left with only more marginal deposits.
The UK hasn't produced enough gas in the North Sea to actually run the country for a very long time, maybe ever. Anybody who sells you a dream about British gas for British people isn't telling you the truth and it doesn't matter whether they are lying or incompetent, you can't trust anything they say.
America, Russia and a handful of other places could do this. It's probably a terrible idea, but it is technically possible. However Britain is not one of those places.