Hi Ms.Basset
Your New Style ESA payments are deducted £ for £ from UC. So any increase in ESA will lead to a reduction in UC. The bad news is that any increase in UC is taken off the Transitional Protection. This is a deliberate design policy of the previous Tory governments to cut the Benefit bill.
David
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
