I had no literature on mushrooms with me; So, I decide to apply the key provide by
British Mycological Society - https://www.britmycolsoc.org.uk/ :
PATRICK LEONARD: SYNOPTIC KEYS TO BRITISH SPECIES OF LACTARIUS, 2008

The answer from this key was: Lactarius vellereus

Application of the key
A H J L R V Y
| | | | | | |-> Y [Broadleaved trees -Habitat]
| | | | | |-> -> V [Other weaker smells including acidic, fruity or none - Smell]
| | | | |-> -> -> R [Un-zoned - Cap markings}
| | | |-> -> -> -> L [Cream and pale buff or pink colours]
| | |-> -> -> -> -> J [Smooth - Cap edge]
| |-> -> -> -> -> -> H {Mild - Milk Taste]
|-> -> -> -> -> -> -> A [White and unchanging - Milk Colour]

Key 7 AHJL RVY

1. Cap predominantly white or cream 2
   Cap rusty tawny, cinnamon, or brick 3

2. Cap viscid, stipe soft to firm pallidus 74
   Cap matt, velutinous, stipe hard vellereus 252

3. Flesh brown with sulpho-vanillin, with beech subdulcis 194