What could be the reason for a feeling of speed oscillation after takeoff in a 747?
There are a whole bunch of possible reasons.

The first thing to note is that, from inside the cabin it can be very difficult to tell the difference between speeding up/slowing down, pitching up/down, and the rise and fall from turbulence (particularly when in a climb). And one I wasn't aware of but as pointed out by Sami, the air conditioning pressure varying because of a malfunction in the engine bleed or pack valve.

So why could it be happening?


Turbulence causing the aircraft to gentle rise/fall, which, in a climb, is fairly akin to small acceleration/decelerations - both to our inner ear, and in terms of what's physically happening to the aircraft
The air conditioning pressure rising and falling more than usual rather than maintaining a constant pressure
Slight pitch up/down manoeuvres, possibly from a relatively inexperienced pilot flying the aircraft
The auto-throttle throwing a hissy fit or, if climbing at 250 knots under 10,000 ft, oscillating slightly in order to stay at/below the 250 knot speed limit
The pilots adjusting thrust manually, possibly for the same reason as above
A gusting head/tailwind. Particularly noticeable near the ground and when in a climb, and can cause a feeling of acceleration/deceleration.
A malfunction in one of the engines causing the power to vary slightly. It's possible this was only noticeable at takeoff/climb thrust levels, and disappeared when throttling back


Typically you'd expect it to be due to either turbulence or a gusting wind, but there are several systems which could develop a small, fairly benign fault and have this symptom.

Edit: As noted by user Jamiec, Storm Katie (a reasonably strong storm) was over the UK at the time, which would certainly back up turbulence/gusting winds being the most likely culprit