To think that I could find a nice holiday on a tight budget?!

Another option could be Interrail passes, and leave the country with Eurostar. A 4 day pass is about £220 for an adult and £180 for a "youth", plus unfortunately you have to pay a supplement for Eurostar on top of that- 180 euros return for the 3 of you. (And a lesser supplement for high speed trains in some countries).

That could be enough to take you to the S.of France and back, or a lake in Austria, somewhere picturesque in Germany etc etc....somewhere with reasonable accommodation costs. It gives you the possibility of interesting stopovers if that would suit, or if you don't use all your days getting there and back you could use them for a day trip.

You can still get reasonablely cheap fares to Italy, Spain etc if you are flexible with your days.
We've booked 9 days in a small town in Spain. Our original plan was 6 days but the return flight was way cheaper 3 days later, and the accommodation only a little bit more for the extra days.

It did take hours of searching and putting in flight dates until I hit on the sweet spot for length of time and cheap flights.

We plan on mainly self catering, just as we would if we were home anyway, and food is cheaper there anyway so another bonus.

We're all just living our holiday wishes through you. Happens every year when someone asks about holiday ideas. We all suggest holidays for you but we are really dreaming of holidays for ourselves😁

Plymouth- Roscoff would be about £500- 800 return in the summer holidays (Brittany Ferries have a monopoly 😬). They do do deals where you can go for a 5 night trip for much cheaper, but I don't know if they do them over the school holidays.

How would your autistic DC be with their own personal tent OP?

We flew to Bilbao 10 years ago and took a taxi to a campsite called Playa Arenillas. We had grand time. Clean, secure, quiet campsite next to the beach. Little campsite shop and cafe. Coffee was 1 euro, ice cream 1 euro. We cooked all our food on the little camp cooker. Nearest town 30 minutes away by hourly bus. You can get a tent and sleeping bags very cheap on Ebay

Where are you located so we can check airports. You need to think out of the Bix a bit to get value.
Do the children like culture and history and local parks etc or are you thinking beach bars and night life.
If it's culture and history and local events you could do the Baltic States or Poland. Public transport is cheap and good on these countries so you can get out and about and see some fantastic sites. They do civic culture much better and often have free events in the evenings. In Lithuania we did open air cinema, a music event, and two national museums at no cost last year. There's always river cruises and recreation on the rivers in the bigger cities. Self catering is reasonable too.
Northern Romania is stunning and the legacy of Ottoman and Austrio Hungarian influence make the history and culture brilliant. Great value too.
What's your basic criteria for activities.

They have quieter sites too, it’s not all party central - the ones near lakes rather than with their own pools look quieter. The end of August is often cheaper, depending on how flexible you can be with dates.

Also look at Top Cashback/Quidco and similar, as you may be able to get more money off that way.

I’d look at Eurocamp - we have a child with ASD and need separate rooms so we get a three bed caravan. We’ve done ferry to the Netherlands and Eurocamp for 7 nights, which we could have done for around your budget including spends when there if we’d gone Dover-Calais and driven up rather than Harwich-Hook of Holland. If you’re flexible on location, look at sites in Northern France and Belgium.

Other option might be somewhere like a city break in a place that’s cheaper, like Budapest, Poland or the Baltics?

Turkey all inclusive could be worth it, especially if you go just before the kids break up

I’d go for whatever flights are cheapest on skyscanner and then a cheap airbnb.

Skyscanner and choose the 'everywhere' option. The really early and late flights are still very cheap.

Travel to destination is quite a big part of costs. I would first think about this.

Look at the low cost airlines and see what they have available without being too picky about destination. You shouldn’t need to spend any more than 500 for flights and luggage etc. Then accommodation I’d say that you’d find quite a lot of self catering apartments available in the Mediterranean for around 700 or less. That leaves 300 for food and extra stuff.

I don’t know how much it costs to take a car over the channel, but if it’s reasonable and I were a competent driver I’d also look at somewhere like
Brittany, France.

You also get to select the airport

I did a quick search and found loads of self catering in Spain holidays ...five nights in august coming in at just over £1k for one adult, two children

I did the Groupon £99 for my family. It’s basically the mystery tour of the world. You need to barter when they call but it includes flights and accommodation. We got Venice, you just need to have a computer to hand to negotiate the hotel. Another option is joining a homestay group
Best of luck, I also have a child with autism so understand your dilemma. and costs of needing a break. You’ll do it ✨

Where do you live / neat which airport?