If you are looking for state (free) school places, there is little you can do other than research areas.
The LEA (Local education authority) is obliged to find you places for all your kids, but the places will depend on which schools have spaces once you have an address in England. The kids could end up in different schools.
Whilst it is a system that has a number of issues, all English state schools are inspected by OFSTED. They rate them Outstanding/Good/Requires Improvement/inadequate. I would look for an area that has several good schools, rather than focus on an outstanding school, as it is likely to be full. Bare in mind that some schools have not been inspected for a long time (nearly a decade in the case of my kids school), and so could have changed dramatically from the report. All reports are available online.
When we moved, I contacted the LEA a few days before our flight - as we had an address at that point. We got an excellent response, with a list of schools with spaces in the years we needed. We then applied knowing what was available. Note: all spaces are first come first served. A place that is available this week may not exist if you wait a week to apply. You then need to be in the school within a few weeks - so don't apply too early!
Are the twins 13 now? How old will they be on 31 August 2024? If they will be 14 by that point, the schools will have started teaching a 2-year GCSE course. I would prioritize their school. If still 13, it's not quite as vital they are in school as soon as you can arange things.
Good luck. Schools were one if the most stressful bits about moving, because you can't really do anything about it until you have committed to everything else.