Encouraging orchid species to grow and increase within a particular site can be part of what are often and variously called:

For a discussion of what these often ill-defined terms might involve see Rewilding & other methods of ecological restoration/Orchid Meadows and rewilding.

HOS strongly advises that when orchid introductions take place outside of a domestic garden there should be clear planning and stated objectives. The greatest care should be taken with what species are introduced and how introductions are recorded and monitored. Successful introductions should be reported to your County Recorder or to Botanical Society of Britain & Ireland (BSBI).

For a guide to the plant recording system and the role of BSBI see Current status of Botanical Recording in Britain and Ireland.
Regardless of the scale or ambition of your project encouraging, protecting and introducing wild orchids within a plot will require some practical steps.

Choosing a suitable site for orchids
Orchids grow best in impoverished soil, but other factors are significant including aspect, rainfall, drainage and pH. The presence of the correct mycorrhizal fungus in the soil is also significant to a greater or lesser extent depending on the species of orchid. Former agricultural land and domestic lawns which have been regularly fertilized  will not support the more sensitive species of orchid but regular cutting and removal of the hay may reduce competition and stabilize or slightly lower the fertility enough to allow more robust and locally common species to establish.
Removal of the top-soil has been used but is extremely expensive due to transport and disposal costs as well as being environmentally questionable.
If there is historical evidence of a species occurring locally then reintroduction might be considered bearing in mind that there will be no knowledge of why the species was lost or where, on a large site, they originally grew.
For information on where in the UK orchid species occur:

Introducing appropriate species
A landowner can plant anything on their land unless it is a banned plant e.g. Japanese Knotweed or a protected species.
Orchids are introduced into a site either as seed or as plants.
Your project will be most successful if you grow orchids known to occur locally as these will be most likely to thrive in local conditions.
Introducing seed or plants only found elsewhere in the UK  and foreign seed/species is controversial and advice is to not plant or sow non-local, non-native species.  If species are to be found locally then only locally sourced seed or plants should be used so the genetic variability of plants on sensitive sites nearby  such as nature reserves and SSSI’s is not compromised. As bees forage over at least a five-mile radius this should be up to within a ten-mile radius. Any successful introductions should be notified to your County Recorder or to BSBI.
Obtaining orchid seed:

For information on introducing orchids by seed see Creating an orchid meadow using seed. Also on YouTube
Orchid species can be introduced as mature plants  although success may be limited unless the plants are maintained carefully through their first couple of years in soil. Symbiotically raised plants may be more successful as the appropriate mycorrhizal fungus may not be present on your site.
HOS runs  a workshop annually on propagating orchids from seed.

Encouraging existing species to increase
Reducing the regular mowing of garden lawns and restoration/clearance of overgrown sites will sometimes allow orchids that have survived underground to complete their life cycle; flower and set seed.
An example is Plantlife's No Mow May campaign.
To encourage these to increase and spread:

Maintenance of an orchid rich site
Whether orchids are found to be present at a site or are introduced, the area in which they grow will need maintaining in order to support and increase their number.
Competing coarser grasses and plants must be controlled by mowing or cutting at times appropriate to the species of orchid present and the cuttings removed.
Use of insecticides and other chemicals should be minimised to protect the balance of organisms present.
Advice on managing a range of landscape types, particularly larger areas and habitats can be found at Plantlife.