Being on a slope won't affect your house being open plan. Open plan is usually created by removing walls between rooms.

Can you post the floor plan too?

Here’s the existing floor plan, and here’s a (rubbish!) mock-up I’ve done of what I’d love to do, I’d love to extend out to give more room for a big open plan kitchen/dining but not sure how this would work with the very low garden!

How far out would the extension go? Doesn't look like very much, but you'd also need to consider where you "land" when you go out of the bifold doors - would you want a terrace at that level? It's certainly not impossible but would require new retaining walls to be built in order to provide the firm footings for the extension and terrace, plus you'd need to think about steps down to the lawn which would be a substantially bigger drop than before. If there's no side access, the groundworks would be tricky as there's nowhere to get a digger in - but perhaps there is access? I'd get an architect round for an initial consultation to see what's possible. Also not sure what width you have and whether that's enough for a run of units, island and dining table - do you know what the width measurement is? Bear in mind you'll need about 600mm for the run, 1000mm (ish) for a gap, 900mm (ish) for an island though it could be a skinny one at 600mm, then possibly 3500mm for dining table and chairs which you can walk around on both sides - so that's about 5700mm minimum if I've done my sums right (though a bench arrangement on one side can minimise the dining space. I seem to remember that @rinked has some handy measurements for minimum sizes of tables & chairs.) But an island is not the be-all-and-end-all of a lovely kitchen - you may be able to create something you love with runs of units and a dining table in the middle. BTW I don't think the garage is actually there, is it? It's just that it's put there on the estate agent's drawing and has stayed on your drawing by accident?

The garage is here to the left! You can have a look at the garden here if you want - https://seekbeak.com/v/p9z67vnAjQk - I love these things! Thanks so much for your help.

Yep I meant it's not positioned right outside where you want the kitchen/diner to be.

Hi Alex, we recently provided a first time buyer with a budget cost estimate for similar works. The budget cost estimate provides a detailed breakdown of works and expenses as well as highlighting potential areas where you can save money. They were then able to determine whether they wanted to go ahead with the purchase of the property. If this is something of interest please send the plans and photos to hello@nestestimating.co.uk and we can provide you with a quote.