Hi Jim.
I'm sorry to say but I don't like non original equipment. I know the Halfords one is cheaper but i'd much prefer you had a genuine Toyota one on your engine. Yes it is costing you money but if it cures the problem obviously is a better deal. Personally i'd replace that Halfords one for a genuine Toyota one. Incidentally the Halfords one, you do know belonging to the Toyota Owners Club you can get a card which will give you about 25% discount, I have one, they are free and last for life. To get a card just join the Premium member discount part of this club, there's a tab on the first page of this site. https://www.toyotaownersclub.com/?_fromLogin=1 it's the green tab.
The rubber part of the filter is a pump for priming the system, try pumping it until it goes hard to see if the engine starts straight away , worth a try.
I know someone who seized up his Toyota Celica just because he had a Halfords filter one on there and the parts person assured him it was the correct one, it fitted but lacked a non return valve which technically wrote his car off.
Regards, Mike.