The solution to the worked example

Over the past few days we have been looking at how we might solve:

VKMHG QFVMO IJOII OHNSN IZXSS CSZEA WWEXU
LIOZB AGEKQ UHRDH IKHWE OBNSQ RVIES LISYK
BIOVF IEWEO BQXIE UUIXK EKTUH NSZIB SWJIZ
BSKFK YWSXS EIDSQ INTBD RKOZD QELUM AAAEV
MIDMD GKJXR UKTUH TSBGI EQRVF XBAYG UBTCS
XTBDR SLYKW AFHMM TYCKU JHBWV TUHRQ XYHWM
IJBXS LSXUB BAYDI OFLPO XBULU OZAHE JOBDT
ATOUT GLPKO FHNSO KBHMW XKTWX SX

By various means we discovered that the key was 6 letters long, and by two methods we determined what that key was. The key turned out to be ‘Womble’.

BEAUF ORTAN DVIGE NEREB ECOME MUCHE ASIER
TOANA LYSEW HENTH EREIS ALOTO FTEXT TOWOR
KWITH THISA LLOWS USTOU SETHE REPEA TINGN
ATURE OFTHE KEYTO OBTAI NMANY VALUA BLEST
ATIST ICSON CETHE LENGT HOFTH EKEYI SASCE
RTAIN EDORP ERHAP SGUES SEDAT THENG ROUPS
OFLET TERSA KEYLE NGTHA PARTC ANBEA NALYS
EDASI FTHEY WEREA CAESA RCIPH ER

Reformatting this, we get: "Beaufort and Vigenere become much easier to analyse when there is a lot of text to work with. This allows us to use the repeating nature of the key to obtain many valuable statistics. Once the length of the key is ascertained or perhaps guessed at, then groups of letters a key length apart can be analysed as if they were a caesar cipher"

Actually, with Beaufort the groups of letters are a combination of atbash and caesar.