Is your second yoga studio on the 6th edition ADLS lease with clause 27.5?
If so, then it is up to you and your landlord to negotiate what is a fair portion of the rent to pay. In my opinion this would be 20-50% of your current rent as your landlord is still providing the premises for you to store your chattels and equipment there.
I assume your second yoga studio does not have the clause but the landlord has offered a rent reduction. I would review your lease to see what terms there are you can rely on eg force majeure and frustration – also google these – there are various articles and commentary across the web. Also google rent abatement – there are some good articles on how to negotiate a rent reduction.
In negotiating with your landlord, I would adopt a practical approach – how much can you afford to pay and how much can your landlord afford to reduce the rent to? It is in both your interests for your business to survive, otherwise, the landlord has no income and the building reduces in value because it is empty. The landlord may be able to negotiate a reduction in mortgage payments with his/her bank which would then enable them to reduce the rent to you.
Be transparent and open with your landlord about your cashflow and ability to pay. Adopt the approach of not wanting to transfer your cashflow problem to the landlord but wanting to agree a mutually acceptable solution. What can you offer the landlord in exchange for a rent reduction – extend your lease, agree a renewal etc?
Whatever you agree to, you want to be able to commit to, otherwise, it is easy to destroy the relationship by not honouring commitments.
I trust that helps.