The accuracy of the meters vary, even when following the instructions to the letter and used only distilled water. The pH reading can even change depending on how long ago you soaked the soil.

You can confirm or see how far out your meter readings are by using the little colour change pH testers, they aren't terribly sensitive either but do generally provide a reasonably accurate test, accurate enough for gardening anyway. Again ensure you use distilled water, they don't always not that on the instructions.

Plants and their tolerance of pH as you know varies, however, they won't die suddenly if they are in the wrong pH, they will suffer because they won't have access to their required amount nutrients and trace elements so it's noticable through the plants reaction such as leaf discolouration or overall health.

You obviously know you need specific pH requirements for your Blueberries and that your asparagus has a more restricted range than most and that you need to know the soil pH before deciding how best to keep them so I suggest the little colour test tubes and distilled water I mentioned above.

Electronic pH meters seem to vary hugely, and give only a very rough indication. I used one recently and found it had no correlation with the results I got using rigorous chemical analysis, so I would recommend using a full-blown chemical-based soil testing kit before pronouncing on your garden's pH.

The general rule is that a clay soil is acidic. I used to garden Wield clay in West Sussex, which was criminally acidic (let alone badly drained and heavy to work). But then it does depend a bit on the parent material  a chalky clay may be alkaline, usually only slightly so. However, poor drainage, usually associated with a clay soil, can increase acidity.

The part of the garden which has been regularly worked has probably had lime added to it over the years, which is why your preliminary results are reading as alkaline. Liming helps to create a good soil structure in a clay soil, and needs to be continued to be added if you regularly manure your soil in future to counter any increase in acidity which almost always ensues. Be sure to test your soil pH before liming, however, as it is possible to overcompensate. I have known old boys who have limed their allotments routinely annually and have ended up with a soil which was excessively caustic.

"Most of the readings are about 4-5, then I get the occasional 8 and a few 7s. This can all be within the same 20cm of soil"

Most likely a natural soil pH of 4-5, but with isolated pockets of high pH due to builders' rubble (= alkaline mortar) dumped in patches when the house was built. Very common, and a far more likely explanation than the pH meter being wrong.

Resin

Soils in Leicestershire are mostly red boulder clay (acid or very acid) on the west of the River Soar, with more chalky boulder clay (neutral to alkaline) on the east side. The more red your soil, the more likely it is to be acid. You can convert areas of acid soil to be alkaline fairly easily with lime. If you soil was alkaline then you would really want to replace fairly large areas before you would grow blueberries.

There are plenty of alkaline clay soils. My subsoil is a blue calcareous clay. There are also many calcareous clays along the upper parts of the Thames.

One advantage of the chemical test kits is that you will get an average reading for your soil while the probe only reads the bit of soil it is stuck in. You might wish to collect a dozen or so samples from around the bed, mix them together thoroughly, wet appropriately, and then stick the probe in that. A chemical test would still be a useful confirmation, and worth the fiver it will cost when you are going to spend a bunch of money on correcting your soil to the necessary pH.