UK Property Law
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If you are able to find the beneficiary of the covenant (ie. the person/body who originally imposed the covenant) then they would be able to release/modify the covenant so that the restriction is no longer in force. Note though that the body in question may very well charge a fee for the release.
If the covenant was taken for the benefit of a piece of land which has now been divided between several owners, you will need to obtain the consent of all the present owners of the that land. If this includes the "village resident" to which you refer then he would be able to contest it on the strength of the covenant. If it does not then he wouldn't (note he may have unrelated rights to object if you submit a planning application to a local authority though
Note that you may be willing to take out a restrictive covenant indemnity policy if you can't find the owner and anticipate breaching the covenant. You can search for providers online and obtain a quote.
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The other village residents who have not had the benefit of the covenant (ie. they own there land independently of the field) will not be able to object on the basis of the covenant. They may be able to object under planning law but as I am sure you will appreciate this is separate area, and if the district council are happy with it being used for commercial use then the objectors have considerable mountain to climb this respect..
The final possibility to remove covenant is to apply to the Lands Tribunal, this is somewhat protracted and extremely expensive (eg. £10-12,000.00). This is only really used by developers or extremely wealthy individuals. The above aforementioned method of removal is a much better way forward.
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