Typically when a market power test is undertaken the competition authorities look at a range of things. These include prices in the market, the quality/level of service provided, investment in the product, evidence of a lack of innovation etc.
There is some evidence (by no means compelling, yet) that BA has a degree of market power in all of these respects.
On the pricing side, there is evidence of higher yields at LHR, and the existence of high slot values could be seen by regulators as a clear indicator of excess profits ('rent' in economists' speak).
On the quality/service side, I detect an increasing amount of dissatisfaction with BA. The Flyertalk discussion on BA is interesting, suggesting a trend of reducing costs and service in a wide range of areas. The BA ground operation at LHR is particularly poor, suggesting that they don't have to try terribly hard.
On the innovation/investment side, BA used to be a clear innovator, particularly in the premium product. Now they are very much an also ran, losing out even to the U.S. carriers in the long haul business class product.
I'm not saying that things are yet at a stage where the competition authorities will step in. But in my experience things can easily get out of hand - it only takes a few politically sensitive incidents for attention to be focussed on any large company. And once you lose control of the agenda, any outcome is possible.
BA/IAG would be ill-advised to assume that they would have an easy ride from the competition authorities if they hold c60% of the slots at a no-R3 Heathrow with an increasing imbalance of supply and demand.