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In my kitchen I would like to give myself some more worktop space by filling a gap (of approximately 55cm/21.5in) between two cupboards with an additional piece of countertop. The cupboards either side of the gap already have a worktop installed which I don't want to replace as I'd like to keep this as a simple job, not replace my entire worktop).

I've attempted to recreate an image of the scenario (with the gap to be filled in the middle) below (sorry for the low quality, today was the first time I've ever used SketchUp!). To the left is a cupboard which is joined onto a wall on its left side. To the right is a small wine rack and then a cupboard to the right of that. Behind both is a wall.

I don't wish to add a cupboard in this gap since it will be used for a tumble dryer, I just want to make the work surface semi-continuous (I am okay with using joint trim either side of the new piece of worksurface).

My main issue is that the existing sections of worksurface are flush to the panels either side of the gap, so there's nothing for my new section of worksurface to be supported with. I had thought about using "L" brackets, but was concerned about which size brackets I would need and how strong it would actually be.

I had also thought about perhaps adding two or three pieces of wood (e.g. 2x1in) equally spaced across the gap at the top of the panels and fixing them with screws to the cupboards either side so that the worktop could sit on them instead, although I wasn't sure if this would be any stronger than using "L" brackets.

Is there a easy-ish way for me to do this? I'm not a DIY expert by any means, but I am happy to give things a good crack.

The easiest way to do this is buy a piece of 1x3 lumber. Cut a piece to go across the back and screw to wall (predrill your lumber). Put a piece in each side and screw to cabinets. You do not have to make your sides the full length - you can hide the ledgers and make the counter look floating.

If you know your counter material you can deduct that to get the height of the boards you are drilling in so your counter matches flush on both sides. After your ledgers are done you can glue or screw the counter down or even use finishing nails depending on counter material. b

This is a very non-invasive method that will cost you $5-6 in lumber and 6 screws plus a little wood glue. This will look better and won't sag and will assure that counter meets up well with existing tops.

Battens screwed to the side (and possibly the back if you want belt-and-braces) is what I immediately thought of as I started to read your question.

It probably won't be stronger than L-brackets, but it will be a lot prettier (and probably cheaper too).

Make sure that you use the right sort of screw to screw into the cupboard sides - if they are chipboard, you need a chipboard screw)

Either wood or L brackets will work for the supports. I'm not sure which one would be stronger; the weak point would probably be the attachment of the brackets to the existing cabinets. I would use L brackets just because they take up less space - this could be important if you plan to put an appliance under there.

You probably don't want to attach the new counter to the supports, just lay it on top. There'll be gaps between the old and new counters, and if the new counter is not removable, it'll be impossible to clean out those gaps.

You haven't mentioned what material you want to use for the new counter. I'd get an unfinished butcher block and cut it to the right size, but that's just me.

Use a multitool machine (vibration cutter) to cut a tiny slot just under the existing counter top on the base units.
You will need to cut four slots.....two each side - front and back.
Then slide four metal strips/flat mounting brackets under the slots.
If a tight fit is found to be is made then your good to go.
Otherwise you might need to fasten the plates under the existing units.
I'd say that the plates need to be 100 mm x 50mm x 3mm thick at least.
Could also be glued in place