Garage conversion ground lintel installation

Hi,

So I've had plenty of advice on here (thanks!) about the best solution to converting my garage. I'm going with the lintel option but was aiming to do a brick and block and have 2 lintels, rather than a brick and batten wall and only having 1 lintel.

However, I'm not sure I'll be able to do brick and block as the walls i'm trying to tie into are single skin on one side. See photos below. At the very front you’ve got the brick length as the depth of the corner and so no issues getting one in there. But going further back means you’d be into the single skin on that side. It’s double skin (house exterior) on the other side so it’s just this wall that’s the problem.

Am I right in thinking I can’t do a brick and block? Thus, I’ll need to do brick and then celotex and batten walling on the interior?

Forgot to say, the slab is too shallow to build on, regs said it needs to be 6 inches at least. Which is why i'm going with the lintel route. I imagine my only choice if going the lintel route is to fit a single lintel and thus i'll have to batten the wall internally instead. But interested to hear alternatives. Cost is a factor though!