What could cause an irregular climbing pattern on takeoff?
The brief period of leveling off is not unique to the flight on that day. Looking at track logs for previous days, it always levels off at around 7,000 feet for some period.
As Terry commented, this is most likely to deal with the congested airspace. Other routes coming into and out of the London area probably pass through the same space, and keeping flights departing Stansted at a lower altitude prevents them from interfering with other traffic.
Looking at a standard departure chart, there is a warning box:

WARNING
Due to interaction with other routes, do not climb above 5000 until instructed by ATC.

This looks to be the route followed by this flight, at least to the DETLING VOR, so it would be expected that ATC will need to limit the flight's climb until clear of other traffic.