See example 9 of HS283 here. This applies to a residential property sold by a UK resident. Letting relief is the lesser of:
2 the exempt gain which is the sum of that part of the gain covered by the owner's occupation of he property as his or her main home and the gain for a maximum of the last 18 months of ownership when the owner wasn't living there and
3 that part of the letting period gain which is not covered by the last 18 months of ownership which is given as an exempt period as part of 2 above.
If the property was only let for the last 18 months of ownership and the owner had previously lived in it for the entire period of ownership except for the last 18 months of ownership, the entire gain would be tax free and no letting relief would be due.
In your case, if you use the April 2015 value as your cost whicb it has to be said is about the most generous tax relief ever given to an individual, you ignore the previous period of ownership as if it never existed. In effect, you are treated as having bought the property on 5 April 2015. However, as the property has been your main home pre-5 April 2015, you will get the last 18 months of ownership as a tax free period if you sell it by 6 October 2016. If you don't, then to qualify for main residence relief for any tax year starting on 6 April 2015 you need to spend at least 90 days living in it during the tax year. If you do that, you get full main residence relief for the tax year and letting relief is not required.
If you based your calculation on one of the other options, then main residence relief and letting relief would play a part assuming the property was let.