Re: A bit rich...
One of the teasmades on Amazon (when I bought mine) came with a little stainless steel thermos jug for the milk. Or you can buy those nasty pods of UHT stuff (or even just a little glass bottle of UHT), if you're not too choosy.
This was the reason I didn't buy a teasmade years ago. But I've been taking my tea black for a couple of years now.
The other, surprisingly nice, option is to go for fruit teas. The objection to these is that they smell far nicer than they actually taste. Which is even before someone has questioned your manhood. It's actaully really nice to wake up to the whole bedroom smelling of raspberries. And I rather like the refreshing first mug of fruit tea, as a nice palette cleanser, giving me the required fortitude to face getting up and schlepping to the kitchen to make a pot of the real thing.
Twinings fruit teas are disappointingly tasteless. You have to leave the bag in for about ten minutes, then they start to become harsh, before they've even developed much of a flavour. Whereas Sainsbury's fruit teas are cheaper, and much fruitier. You can take the bag out after a couple of minutes, and they've achieved a nice strong fruity taste. I haven't got round to trying any others yet.