Hi there - I do know what you mean about the one hand on boob, one on baby situation - I fed like that for the first couple of months until I could take one hand off baby - and now he's a nosey 18 wk old I have to keep a hand on him again otherwise he'd crane his neck and fall off my lap if someone interesting walked past!
Does mean my lunch goes cold in cafes a lot, it's true.
I use a nursing cover quite a bit in public (derided for some reason on MN, very very common in the USA and my hometown - where BFing is also prevalent). I like it because then I don't have to worry about being discrete - I can have ungainly boobs flopping around the place if I need to, to get the right latch -and I'm not flashing anyone.
I don't always have it with me, however, and I've got some breastfeeding tops (from motherwear.com, don't know if the UK has equivalent not-too-pricey versions, I hear H&M has a line?) which also help. Some people swear by the vest-top-underneath-a-real top method: you hitch the vest top down under the breast and then the real top UP, and the baby's head covers the bit of boob that's actually out. In that instance, you might still be holding your breast but you'd be holding it through the top layer shirt, if you see what I mean..
Glad BFing is getting easier for you! I found 6 wks so much easier than 2 weeks, and at about 10wks it was practically enjoyable! Now it's easy as falling off a log (or a lap!).
Hope some of my ramble helps. Must go back to bed!