My approach has been to use a loyalty program - good rates (I've never seen any of the aggregators beat what I pay), points for free rooms, and less hassle if there's an issue. I usually use Wyndham Rewards, since that includes the Wyndham Garden and La Quinta, but I'm sure that anyone's preferred chain has one.
The OP mentioned just wanting a room for Tuesday; I just checked Wyndham's hotels in York, and there are several places available. Wednesday and Thursday are the hard nights. Checking at the last minute sometimes works - might snag a last-minute cancellation.
And as @Andy Hummell mentioned above, be sure to read the reviews.