Can anyone recommend a Saas based logging tool which can handle application logging and telemetry as well as infrastructure health etc?

I'd recommend Solarwinds Loggly. 

you may have a look on Dynatrace SaaS version or Dynatrace platform subscription. 

we are using cloud platform logging and monitoring tool, before choose other SaaS solutions, in order to reach a clear understanding of what it is our requirement: we wish to understand if we need a single and standard cross cloud solution, or it is better to reach a simple baseline, and get a more focused and integrate solution where it is important.

Splunk or Datadog

I believed you are looking for a SaaS-based observability tool. Splunk Cloud and Elastic are 2 products that might be able to fulfil your requirements. The usability and ability to support out-of-the-box (without much customisation) for different types of log sources should be among the key criteria for your product selection.

These 2 products also have security modules that tightly integrate with the observability modules to provide an integrated view of both infra and security posture, facilitating Investigaton process.