There are measures for dismissing someone fairly if followed properly. It can be lengthy though it sounds as though they have been trying to make appropriate adjustments.
Try ACAS, they have lots of guidance on their website and a telephone helpline.
http://www.acas.org.uk/index.aspx?articleid=1461
Are there any associated bodies with the charities they could get legal advice from or could they get their own legal advice? Each company can be different as to what is reasonable in relation to the employer and employee so some bespoke advice and ensuring everything is on a formal footing where appropriate and properly documented to avoid a potentially lengthy and costly tribunal claim.
A lot depends on the process, not necessarily the reason, for a dismissal being fair although compensation can be reduced or even effectively wiped out if contributory factors are involved.
Unless there has been a recent change, the loser pays the winner's costs does not work in Tribunals as it does in civil claims so a Tribunal can be a costly venture, even if they win, so avoiding that would be best if possible.