When you want to convert between miles and kilometres, you could do what I do. Remember that it's 150 million km or 93 million miles from here to the sun, and do the appropriate maths.
(Actually, true, I
do do this. Although I ofte shortcut it to 31 miles to 50 kilometres, or reduce it down to 0.62 ml to 1 km or 0.93 (effectively 1) miles to 1.5 km, depending on what I'm converting. And you ought to hear my method for converting between Fahrenheit and Celsius!)
I'd actually (even more seriously) suggest the benchmarking method, already suggested. A box 10cm on a side contains litre, which would be 1kg of water, with a box a metre long on a side containing a tonne(/metric ton) of water. Base that upon the metre being around (a factor of 1.1-ish) a yard, and ten centimetres being roughly a third of a foot, or so on depending on which measurement you normally use for any given scale.
But, to be honest, you'll be rarely asked to look at something and then tell them how big/long/heavy it is. And then, eyes rolling upwards in exasperation, they'll ask you
again, but this time want it in metric/SI. When accuracy matters you'll have your micrometer, laser-rangefinder, scales, weighbridge, flow-meter, anemometer, light-meter or whatever and if it matters that it's metric it'll almost certainly have a metric/SI readout. And apart from doing some quick sanity check (so that if it's more than half an order of magnitude out, you can work out why it measured wrong) or, in some cases where it's important, an immediate re-measurement to ensure you really didn't make an error, you don't have to have quite so much of a grasp of the system.
You
will do, of course. You'll glance at the width of a carriageway and start to give your guess as to its width in metres instead of yards (not that
that's much different, BYGTI). But I reckon the local PD will still appreciate your guess as to the perp's weight in lbs (whereas I would start to give them how many stone they weighed, and have to multiple by 14), when taking the witness statement. I've no idea if you get pints of beer in your bars, but over here beer and milk (at least in 'traditional' settings of pubs and doorstep bottles) are not in litres, although in others (cans and plastic bottles from supermarkets) it's usually in millilitres or litres.
I'd say know roughly what they are, and obviously their names, yes. But you don't necessarily need to work towards being an infallible "guess your weight machine", only calibrated in metric measure.
Now, without using Google, tell me how many US gallons there are to any given imperial one.
(And then tell me what the petrol(eum/gasoline) price that I last paid, of 118.9 pence per litre (the cheapest locally, at present, it can be up to 10p more at another place!), would be in your local standard, and how much
you typically might pay for standard unleaded!
)