My airline pilot friends tell me that even a 747 at max weight climbs at 250 below 10,000 ft.
Your airline pilot friend is wrong.
Our max gross takeoff weight is 833,000 lbs.
I just calculated our takeoff performance using present location present conditions, for a max gross takeoff, and came up with a V1 speed of 160 knots, a rotation speed of 179, and a V2 (takeoff safety speed) of 188 knots. Our climb speed once flaps are up will be 100 knots over V2, which is 288 knots in the climb. We would ask for a high speed climb, and get it (as that's our minimum speed on the climb-out.
According to these calculations, we couldn't raise flaps above our "1" setting if we intended to restrict speed to 250 knots, and we're not going to do that. That leaves flaps and leading edge devices out for the climb and we don't climb like that or predicate climb performance on that.
If minimum safe climb speed is 300kts below 10,000 ft, what's Vref?
Sounds like a long runway is needed whatever it is!
We use Vref for landing, not for takeoff. The takeoff distance on a 12,000' runway, using a reduced takeoff power setting, shows a stop margin of 2,900 feet today. That's assuming maximum reversing and a rejected takeoff no later than V1.
If we did need to dump fuel to come back and land, my theoretical flight would take 51 minutes of dump time down to our max landing weight of 630,000 lbs, a Vref speed of 152 knots, and a landing distance of 8755' (calculated with minimum autobrake setting). That also adds up to a 237 knot minimum speed with flaps up (we use 20 over that, so 257 will be our minimum speed until configuring for landing).
Just for kicks, I ran the same approach to the same runway under the same conditions, and added a trailing edge flap assymetry. Our landing distance increased to 10,844' in minimum autobrakes. Approach speeds bump up 20 knots.
If we leave the flaps alone and let them function normally, but find we're unable to dump and have to land at takeoff weight a fire on board, for example), our Vref speed becomes 179 knots, our target speed on approach is 192 knots, our landing distance in minimum autobrakes becomes 11,827'.
These are actual numbers using the same performance program we use on the line, just installed on my laptop, from the warm comfort of the hotel room. These use the same conditions in which we landed a few hours ago, in the same airplane.
The short answer to your question is that on takeoff, we always see the red lights at the other end of the runway.
What gets up my nose however is how many people are simply non-transponding.
I don't know about the UK, but airplanes without electrical systems, radios, or transponders are still common in the USA. While I encourage people who have transponders to use them, of course, I encourage everyone to use eyes to look for traffic and rely on radios or gadgets to do that for them.
The life you save, after all, may be your own.