If I were to use my home as part business and install solar panels, can the capital be part-offset against profits and if so, how?
To be allowable as a deductible expense against your business taxable profits the particular item must be 'wholly and exclusively incurred' for the purpose of the business. So as the house is not wholly and exclusively used for business reasons the expenditure would not qualify for capital allowances.
In addition your primary residence is exempted Capital Gains Tax (CGT) when it is sold. If you were able to claim items of expenditure such as solar panels as a capital allowance, it is possible that HMRC would challenge the CGT exemption meaning the sale would be chargeable to CGT, at least in part.
See also: Tax for part-time businesses