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1. The legends and letters appear to be quite blundered, so a Danelaw origin seems most likely. The first two letters on the obverse are ED, which is consistent with Aethelstan II (Guthrum) of East Anglia. His known coins are signed EDELIA RE, EDELSAN RE, EDELTA, etc, variations of which would be compatible with the legible letters on the coin. The reverse legend ends in a similar way to the St Peter memorial coins of Viking York (i.e. SCI PETRI MO), but I think the southerly location of the find makes an East Anglian source much more likely.
With regard to the denomination, at 0.5g it can only be a halfpenny, but the large flan size is surprising. The weight is slightly less than a typical Edward I halfpenny, which has a diameter of around 15mm, so the coin must be very thin.

2. Aethelstan Cut Halfpenny. Silver, 0.73 grams; 19.30 mm. +[EDEL]STA.N, Alpha A with bar above within small inner circle. R. [R]EX. A.N.[G]., around Omega within small inner circle. Interesting pellet 'privy marks' on both sides including one within the 'N' on the reverse (not mentioned or shown by JJ North). Probably minted at Ipswich, Suffolk 827 - 845 A.D. Recorded with the Fitzwilliam Museum at Cambridge University as: EMC TBA. S 950; N 439; BMC 19. Very Fine and better. Only three similar coin with the barred A recorded with the Medieval Coin Corpus (EMC) at the Fitzwilliam Museum and Sylloge of Coins (SCBI) of the British Isles, and None with this privy mark configuration.
It is not known how Guthrum consolidated his rule as king over the other Danish chieftains of the Danelaw (Danish ruled territory of England), but we know that by 874 he was able to wage a war against Wessex and its King, Alfred. By 876, Guthrum had acquired various parts of the kingdoms of Mercia and Northumbria and then turned his attention to acquiring Wessex, where his first confrontation with Alfred took place on the south coast. Guthrum sailed his army around Poole Harbour and linked up with another Viking army that was invading the area between the Frome and Trent rivers which was ruled by Alfred. According to the historian Asser, Guthrum won his initial battle with Alfred, and he captured the castellum as well as the ancient square earthworks known as the Wareham, where there was a convent of nuns. Alfred successfully brokered a peace settlement, but by 877 this peace was broken as Guthrum led his army raiding further into Wessex, thus forcing Alfred to confront him in a series of skirmishes that Guthrum continued to win. At Exeter, which Guthrum had also captured, Alfred made a peace treaty, with the result that Guthrum left Wessex to winter in Gloucester.