I had a search on the National Archives website for the Finsbury Park Act 1857 and there aren't any records. I wonder if it was replaced by subsequent law on public open spaces without being repealed (as often seems to happen in English law).
- Date of Works 1869 - google.co.uk 
- More history - finsburypark.wordpress.com
# Hayes, H. (2001) A Park for Finsbury.
On 5 June 1857 Superintending Architect Frederick Manable gave this report and estimate of costs for the creation of Finsbury Park to the Metropolitan Board of Works.
On 8 June the plans were approved by the board to be submitted to H.M. Office of Works for approval and to be submitted to the House of Commons.
On 18 June H.M. Office of Works approved the bill. The bill became law on 17 August 1857 - finsburyparkstories.wixsite.com
# LOCAL GOVERNMENT, LOCAL LEGISLATION:
MUNICIPAL INITIATIVE IN PARLIAMENT
FROM 1858 TO 1872 - lra.le.ac.uk
The years between the first Local Government Act 1858 and the establishment of the Local Government Board in 1872 saw great changes in England and Wales: growing populations brought growing problems in crowded living conditions, but there were also increasing wealth, manufacturing and intellectual resources in a context of major international influence and self-confidence, and rapidly expanding countrywide infrastructure.
Against this backdrop, the municipal authorities of this period had few general law powers to regulate local conditions, or to provide services. While Parliament was still – at least at the outset – broadly antagonistic to centralisation and the enactment of common standards, it was willing to grant private Acts – special local Act powers – to those places that sought, and could justify and pay for, the means to improve and invest in their localities. This thesis identifies and analyses for the first time the 335 local Parliamentary Bills, and from them the 278 resulting Acts, that municipalities promoted in the years 1858 to 1872 inclusive.
Three things stand out from the huge mass of local statute-book material which these 278 Acts comprise – themselves only a small fraction of the total of private Acts passed in the era of railway mania, and of much else besides. The first is that, far from being an unco-ordinated mass of inconsistent, quixotic provisions as private Acts are sometimes thought or assumed to be, these Acts have a substantial degree of cohesion as a body of material. Secondly, the towns and cities of northern England secured more than half of them. Thirdly, the costs of promotions (and the vested interests involved in them) represented a huge and often wasteful outlay that a more pragmatic and forward- looking Parliamentary attitude could have greatly reduced.