It was won and lost during the time Lord Vyner owned Bidston hall so it was definitely the 1800s, before Birkenhead corporation bought the hill.
Source The Friends of Bidston Hill
Movements in favour of public acquisition of Bidston Hill
were made in 1883 and 1897 – the latter being in connection with Queen Victoria's jubilee; however, it was not until 1893 that the project was taken in hand. The Hill formed part of the estate of Mr Robert Charles de Grey Vyner who conducted negotiations in a handsome manner by taking the lowest of three valuations, making his own contribution to the fund.
In 1907 steps were made to secure another portion of the Hill, which was “on the market”. It was feared that the land might be used for building purposes. The area in question was an area of 22 acres on the south-eastern slope of the Hill, known as the “Pine Woods”. It was acquired as a memorial to the late Mr Edmund Taylor whose hard work and influence made it all possible. The cost was £10,500 in 1907.
Other acquisitions were:
1893-94: the summit of the Hill – 24 acres £5,800
1897: A further portion of 38 acres £11,750
1900 Several smaller pieces, amounting to about about 4 ½ acres £2,260
In all 88½ acres were acquired at a cost of £30,310 (1914). The corporation contributed £14,625 and the rest was raised by public subscription,
On 8 th December 1933, Mr Royden (Chairman of the Bidston Hill
Committee) considered the Rhododendron Gardens would be ‘a grand addition' to the Hill.