One man's enclave is another man's exclave and this list shows that such geographical anomalies are more common than one might expect, even within Western Europe.
Until 20th October 1844 Hereforshire ruled the roost over a small enclave in Cascob parish, eastern Radnorshire. You can just about make out the borders of the enclave at the centre of this old map (pictured).
No doubt Radnorian joy at regaining Litton was tempered by the loss, to Brecknockshire, of that part of Glasbury parish lying south of the river Wye.
Coming up to date, it could be argued that the Shropshire hamlets of Brompton and Pentreheyling be transferred to Powys. Although not enclaves they cannot be accessed by road from anywhere in England without crossing into Wales.
UPDATE: Anon in the comments draws my attention to the Baarle Hertog enclaves in Belgium and the Netherlands. This website explains a complicated situation very well.