I'd of thought the quickest way of doing it is when you're driving, hit up on the d-pad and put the engine into fast mode
As a matter of interest, what circuit are you on ? At Monza you should easily be able to get upto (and a little over) 220MPH on the start/finish straight.
(Assuming Dry Track) - Go to quick setup in the garage and select the setup on the far-right. As above, on the track, make sure the throttle response is set to Fast and you should get it no problem.
Sorry i had a quick read and just replied, i thought you meant for the achievement.
If you arent getting a top speed adjust 7th gear a bit in the setup menu.
Remember to change your gear ratio's on faster tracks. If you are bouncing off the speedo mid way down the longest straight, you know you need more top speed so notch up 7th, 6th and 5th and you will go much faster.
Also consider reducing your downforce.
A combination of both of the above will drastically reduce your lap times too.
I've got the achievement for going over 220mph, and I did it in the Force India using nothing more than the quick dry setup and option tyres. So it should be do-able on the Monza home straight in a McLaren.
I managed to get the 220mph achievement in a normal race at Spa Had the downforce very low, and manually extended 7th gear to make it taller. Got to about 225 along Kemmel straight before I had to break