Here is an article that might help you https://www.idealhome.co.uk/diy-and-decorating/best-white-paint-walls-172455

I'd paint the cabinets white, remove the large cornice around the top of the wall cabinets and replace with something simpler. I'd replace the tiles with something like a matt white metro and update the hardware with black or pewter like you suggested. I think these few, relatively inexpensive changes would make a huge difference and hopefully brighten the space.

Tried to find some photos of white kitchens with wood worktops and black handles below...

I think I'm the only one who likes the colour of the wall tiles! I'm not personally keen on wall units though so would look at something like farrow and ball setting plaster shown here on the walls to blend them in. i personally would look at a grey with purple undertones for the base units, I can't recall this colour but i think it's similar to Charleston grey and would work with the handles you want (I'm not sure that dark base units really darken the room?).

Having said that are the white appliances yours or the previous owners as I would want them to blend in?

I might also remove the chunky shelf and have 2 slightly slimmer and longer ones.

i think its quite hard to make changes for £150 though as your paint alone may cost that. I also think this is definitely one of the best kitchens we've seen on houzz wanting a makeover so you could wait until your budget is bigger?

It depends what your plans are for it long term. I would not replace the flooring as it looks good and would cost a fortune. I would be looking to put up some led lights, Philips do some that give a lovely quality of light that could replace the single pendant. Replacing the wall tiles would be my preferred option, something like a charcoal patterned cement look tile.

I would suggest keep the floor and worktop as they look in good condition and not really out dated. what is the cabinet door made of? if they are melamine, it may be difficult to change to a designer color other than the off the shelf cabinet paint colour. if you do have the choice, consider some classic designer color. Farrow and Ball, Benjamin Moore will be a good starting point. you may consider color in white, grey or sage tone. As you have a shaker kitchen, it is much easy to work with and won't be out dated for a long time. I attached a couple of photos of shaker kitchen in Farrow and Ball with wood worktop. the first one is in Blue Gray, second one in cornforth white.

as for the wall tiles, you may consider clad them with IKEA backsplash, paint them with tile paint or even stencil them. if you are willing to do some more complex work, replace them with some subway tiles off eBay. but I would always be cautious of removing old stuff as you never know what you will find or damage and the cost can easily escalate.

The paleness of the green is creating a discordant effect with the floor. If you want to use two opposite colours I would make the green darker. I don't think apps are accurate enough to give certainty but they do give an idea. I like the off white best, it looks good with the worktop. There are lots of pale neutrals or stoney colours that may work but you need to buy test pots and test them on large pieces of card, preferably A1 from an art shop. If using the teal or green I would go darker.

The off white, nice fresh finish.