If you can grow large carrots it sounds as if your soil is pretty good and fairly light. More likely sandy than clayey. If it were clayey you could take a pinch and squeeze it into a ball and it will crack in dry periods in Summer. To find out the proportional constituents of your soil you can do a simple jam jar test. Google it or follow the link below. As for the chemical composition it is not as easy to find out here as it seems to be in the US where soil tests appear to be widely available. If you Google 'soil testing UK' you will find a few links. Garden Centres sell DIY soil tests for acid/alkaline. Also you can look at local vegetation. Heather, gorse, bracken, rhododendrons, camellias - acidic. Beech woods, wild cherry, scabious, kanpweed, hairbells - alkaline.
But actually most UK garden soils are fairly neutral - extremes are rare.

If the muck is fresh I'd pile it up and cover loosely with plastic or tarpaulin and then use it in the Autumn. If you've had it all Winter you could spread it this Spring. My delivery has been piled up over Winter and I'll spread it as I go along preparing the ground this Spring. Alternatively, if there isn't a huge amount you could mix it into your ordinary compost heap and use it when the compost is ready.

Here is a link that might be useful: Jam jar test

One major problem with those DIY soil test kits from the garden centers I have found is accuracy. Some tell me that a baking soda mixture and vinegar have the same pH and they do not tell you what needs to be done to correct the pH if it is out of whack.
These simple soil tests may be of some help,
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.
2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains’ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.
3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.
4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell, to a point. Too much organic matter can be bad as well.
5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

You could spread that manure on the garden and plant shortly afterwards as long as your harvest is no sooner than 90 days after applying that manure.

HI Amy and welcome. I agree with floral_uk, if the garden does pretty well already and you are not desperately in need of amendments, it may be best to compost that manure so the straw and shavings are decomposed. That will reduce the risk of sequestering nitrogen out of the soil which could do more harm than good. It's hard to estimate whether that's even a problem without seeing the stuff though.

One thing we always tell people is to try things, observe and adjust.