What is the highest altitude a witch or wizard can ride a broomstick? Do they provide some magic to protect the rider from altitude sickness? Of cause this is not a problem in England, but it could be interesting to know if you could cross the Himalayas.
Presumably a witch born & living in the UK would be accustomed to conditions within a couple thousand feet of sea level, and so would need some kind of supplemental oxygen at higher altitudes. Muggles who fly in those contraptions known as aeroplanes can't fly much above 12000 to 13000 feet before they need oxygen; Muggle passengers in planes flying above 15000 have to use it continuously or else fly in a pressurised cabin.
An English witch therefore has a couple options. Without any other kind of magical or mundane assistance, one can fly a broom relatively safely up to 12000 to 13000 feet for a while. Best bundle up, though, because thin air isn't the only problem! (An air temperature of 60deg at sea level might drop to a bum nipping 10deg up at altitude.)
Theoretically, if our witch knows a couple of highly useful flying spells & charms, altitude should pose no particular issue. Naturally, the spell collego aeres and the protego hypoxia charm will be very helpful. And don't forget to keep in mind the high flyer's favourite! -- exfrigerito culos, oo, and also manitepido / manicalido, just in case you forget your flying gloves! Oclos denebulo should round out the necessaries.
Those should get our witch over the Himalayas without difficulty: even Mt Everst at 30000 feet elevation should be quite easy. Should only take her something 4 or 5 minutes to get to the summit.
But, of course, who doesn't want to fly higher even than the highest mountains? Since broomsticks work by countering or nullifying gravity within a local field (broom + mounted rider + reasonable attached baggage), there will eventually come a point when the broom will no longer fly effectively. Gravity decreases as distance from the gravitational source increases. At an altitude of about 8000 miles, our witch would experience 1/4G. Since her broom is designed for optimal operation at 1G, her broom would experience a briefly liberating peppiness at that altitude -- it would be four times as powerful! (Better use that carpe scopa charm real quick, before the broom takes off, leaving her for a long plunge back to Blighty!)
Eventually, the gravitational grasp of Earth becomes so weak that we no longer feel it. At about 40000 miles altitude, gravity is 1/100. I would hazard the guess that as the gravitational pull decreases, the initial spur in broom efficiency will peak and then drop off precipitously. The farther away from Earth our witch flies, the less gravity there is for the broom to work with and thus less force to push against. It would now have to work harder to continue producing any lift.
Main problem for our witch now is that, while inertia will carry her broom upward at its maximum velocity of 100 mph, she'll eventually break through the altitude beyond which the magic within the broom will simply give out. She's now too far from Earth for the broom to push against its gravity; but she's also too high now for Earth's gravity to pull her back down! And she's nowhere near close enough to the Moon to use its gravity to push off of.
Other concerns: brooms only fly at most 100 mph or so. It would take a fortnight for our witch to get far enough out into space to reach the absolute maximum altitude that the broom will function. I would hazard that, even with all the charms and spells, she simply can't keep up physically. She's got to sleep sometime; and is going to have to stretch her legs and eat and spend a penny somewhere along the way. If she flew straight up for a whole day, she'd reach an altitude of 2400 miles; and she'd have to spend another whole day coming down again!
In other words, the highest altitude for riding a broomstick is constrained by the physiological condition & preparation of the witch attempting the deed; not so much the material & magical components of the broom itself.