My hosting company says I need to upgrade

Hi,
I would like to install zen cart to my website but the hosting company are telling me it is not possible because I would need to upgrade. I use 123 reg.
Are they lying to make me pay?
The website is http://heathrowlondonchauffeurs.com and I would like to integrate paypal checkout.
Is there any other easier way?
they say that shared accounts are not suitable for e-commerce websites with cache enabled.

Zen Cart can run okay on most shared-hosting-accounts.

Your shared-hosting may have peculiar SSL requirements, so you may not be able to offer SSL if the server uses proxying to provide SSL capability.

I've no idea what you mean by "with cache enabled".

I can't tell you whether you need to upgrade or not. Your hosting company probably knows better. It would be smart to get the "technical why or why not" behind their claims.

As far as PayPal goes, Zen Cart supports PayPal Express Checkout already. You simply need to do a couple configuration steps to tell it which PayPal account to deposit into.