The other nine seen at least once but only intermittently are clouded yellow, small copper, white letter hairstreak, brown argus, purple emperor, painted lady, silver washed fritillary, marbled white and small heath.
Some of the 28 are more Common than others and the numbers go up and down each year. However, none are very rare.
Most frequently found by far is the speckled wood (top picture) — medium-sized, chocolate brown with cream spots, which can be seen any time between late March and early November weather permitting. Other species have more limited flight periods.
Different species have different habitat requirements. But the best place to look is the Scope while the mown grass areas on the main Common yield little. Some species like the whites are easy to find; others are well camouflaged so it can take practice and some skill to find them.
From the purple, brown and yellow ring eyespots of the peacock to the silvery blue of the delicate little holly blue, all are beautiful.
More information here on local butterflies and on butterfly identification here