amanzi:

 

With martyyn's help, I had a look at this site. As I suspected there was malware hidden in a temp directory. For those interested, here's the idenitification of one of the malware files: https://www.virustotal.com/en/file/6704ee4feec361c4cf382b637313b74e5ea20e800536d4d59497ec8df004ec66/analysis/1489454473/

 

Though there are other valid reasons for moving away from this hosting provider, this particular malware was almost certainly installed due to an out of date Wordpress version, and so it's not directly the hosting provider's fault.

 

Must have been a really old version as older versions get automated updates still. But this is part of the problem with these types of website, they get setup, but updates aren't budgeted for. Many can be updated automatically without any problems, but often things can break after updates, such as themes, plugins etc, which can involved work. So often it is best to do an update on a development server first before applying it to the live site.