Currently, the familiar white-on-brown roadsigns providing directions to tourist attractions are treated as any other roadsign and their formats are strictly governed by the Traffic Signs Regualtions and General Directions act (of 2002). That's OK in itself, but this forces those signs to conform with the other rules in TSRGD which enforce the use of miles and yards onto all signs.
Now, these are signs that are predominantly intended for tourists. A large number of these tourists will be from outside the UK and won't be familiar with miles or yards (as indeed are our own children until they are about 9 or 10 years old).
Make Britain more friendly for our visitors, and change the tourist signs to metric. Don't waste money requiring the old ones to be converted (though that would be an option). Just make it a requirement that all new ones are in metric and that when old ones need replacing that the replacement shall be in metric.
Just metric, not both systems. That would clutter the signs horribly especially in Wales where the current signs have to be translated. ( Welsh for 'mile' is 'milltir' and 'yards' is 'llath'. ) The great advantage of metric in Wales is that 'km' is 'km' and doesn't need to be translated. Other bits may do, but at least the distances would only appear once, and be clearly understood by all.
Why is this idea important?
The Luddites may hate it, the Daily Mail and Daily Express hacks will hate it, but sooner or later all Britain's roadsigns are going to have to go metric. We are already well past the point where half the drivers on our roads were educated only in metric. Just reading the threads on this site show that "K-day" when it comes will be welcomed as long-overdue by many.
It makes sense to plan ahead and cut the costs of that future changeover by phasing the changes in, and here's a suitable candidate-set of signs that could change early (to the country's benefit in the tourist trade).
So – let's make it so.