The Historic England (formerly English Heritage) website includes links to the Historic England Archive which includes maps, drawings, plans and reports for gardens and garden buildings and the full text of many Historic England Research Reports. The link to the section on the methodology of Garden History Research Methods is well worth investigating.
The National Archives is a good place for finding records relating to sites and their owners. Searching is free, but you may need to pay to download documents or to have prints sent to you.
The Support for your research section of the site gives guidance on searching for different types of information. There is a guide to Garden History Records held in the UK
https://www.archaeologydataservice.ac.uk/
Based at the University of York the aim of the Archaeology Data Service (ADS) is to collect, describe, catalogue, preserve, and provide user support for digital resources that are created as a product of archaeological research.
ADS includes full text access to key archaeological journals, CBA Research reports and over 7,000 unpublished fieldwork reports. Garden sites and buildings are included.
This box lists some key web resources on (almost exclusively UK) Garden History that are freely available to all, including information on gardens that may be visited. In the boxes on the left are some sites that are more general but include relevant information for garden historians.
Some useful worldwide garden history web resources are listed below.