It’s not too hard to do, but it’s not really something you can do with a spreadsheet with the TfL system.
If you want to send me the list of postcodes privately**, I could probably do this for you with a bit of code. The output would be a CSV file, which you can load into Google Sheets/Microsoft Excel etc.
I’m going to guess you have a list of possible new locations and you want the typical journey time to them?
Would you be after … walking times? Public transport times? Car times.
Another option is the Google Maps Directions API - https://developers.google.com/maps/documentation/directions/overview - but again I don’t think there is a “codeless” version. You can get a free intro offer from Google.
(Of course, it’s Microsoft who give free stuff to charities) https://www.microsoft.com/en-gb/microsoft-365/nonprofit/office-365-nonprofit-plans-and-pricing
** postcodes by themselves don’t cause a GDPR issues as they don’t identify individuals, but groups of houses.