Then as there is no gain (no profits being made between the value of the inherited price and the sale price) then you will not have a capital gain position to consider.
But, as I imagine, it may take a little time to sell - then all you have to consider is the profit made between these two dates.
If the total profit (on your share) is less than £10,600 then your have NO capital gains tax to worry about in the UK, and no need to declare this to HMRC.
But if the profits are more than £10,600 then make sure you also are advised on
1) Evidence of the costs to sell, such as legal fees and relator/estate agent fees
2) Evidence of any other associated costs towards the sale of these properties
3) Valuations of the property at your mothers death
4) Evidence of the sale price
As 1/6th of any costs to sell the property in Lux and 1/5th of the costs for the USA property can be deducted from your share of the gain.
Also if any taxes are suffered in Lux or USA, then you also need evidence of this too, because if there is a UK capital gain (profits of more than £10,600) then these taxes can be offset against UK tax arising (only equal to the UK amount due, the UK cannot refund another countries tax) as we have a double taxation agreement with the USA and Luxembourg (?)
But I would liaise with whoever is handling the sale for information about that countries tax position on property sales, or the family member who is co-ordinating each sale, to establish this information for you and whether through your non residency in each of those countries, and your intent to declare any gain arising to HMRC, as this is your country of residence,whether they have the ability to exempt you from any form of their countries taxation.
Do feel free to ask any follow up questions