So it looks like the TK aircraft you saw was TK1971
https://www.flightradar24.com/data/a...c-jsn/#8482cd0
If you zoom in to the map you can see it followed pretty much the same course as BA995, so went to the south and then came back in for another attempt,.
From what you saw it sounds like the aircraft would have been around 200-300ft from the ground just as it was about to pass over Hatton Cross. You can abandon an approach at any time but there is a specific point where you need to make a positive decision to land or to throw it away and go-around. At LHR 27L for a normal ILS approach and when not under low visibility procedures that decision altitude (sometimes called "minimums") is 280ft - you can see the figure in the bottom left table in the chart on this earlier post under the CAT 1 DME heading:
http://www.flyertalk.com/forum/25878054-post10.html
It sounds like they were at that point as they were about to pass over Hatton Cross and clearly made the decision to go-around.
When you reach that point if you haven't received the landing clearance from the tower controller (maybe the previous landing aircraft was slow to vacate), or the approach is not stable, or you are not visual with the runway then you go-around.
The actions that would happen in the cockpit are that take-off/go-around power will be engaged (TO/GA), the flaps raised part way from the landing configuration, and pitch raised to climb the aircraft. Once they are climbing the gear would be raised as well.
For 27L the published missed approach course is that they would have continued flying runway heading 91 degrees until they past 1080ft, then they would have done a left turn to 149 degrees and continued climbing to 2000ft initially, then 3000ft. During that time on of the pilots is talking to ATC and they would probably start to get instructions on course and height to get them back in for another approach if the flight crew want to try again.
Hope that helps to explain it a little.