Corbets Avenue
Your alcoves are 147 mm deep on the left and and 178 on the right. Any alcove unit will need to be set back 10 mm from the front of the chimney breast and there is a 6mm back panel so the shallower alcove will be about 130mm deep, as long as the wall/plastering is vertical or leaning outwards as you can easily loose another 25 mm if the walls are not vertical. It can be made like this but you still won't get your sky box inside if it's flat on its base and whether the TV will sit inside is dependant on the bracket. I think the alcove cabinet part needs to be deeper and come beyond the chimney breast. I have had a quote for photo realisation and it will cost £450. My design fee is an additional £200 for the scale 2D drawing needed to work out the design which you will get back if you decide to proceed.
This is another way of tackling the problem of shallow alcoves
Q