At 0835 BST, the FTSE 100 was 0.3% lower at 6,952.54, unable to hold on to opening gains, as the pound rose 0.4% against the dollar to 1.1351. At the same time, government bonds rallied, with yields on the five and 10-year gilts down around 20 basis points.
In a statement on Sunday, former PM Johnson said he had the support to stand but that it would not be the right thing to do and that there needed to be a "united party in Parliament".
That leaves Sunak and cabinet minister Penny Mordaunt in the running, with the former likely to be made PM as early as Monday.
Commons leader Mordaunt has the public backing of just 26 Conservatives MPs, whereas Sunak has the backing of 145. The candidates need to secure backing from 100 MPs out of a total 357 by 1400 BST on Monday in order to make it onto the ballot paper.
Richard Hunter, head of markets at Interactive Investor, said: "The current level of sterling of over $1.13 is a comfortable improvement to the level of 1.03 which it had briefly touched, but a rampant US dollar this year has eroded the price of the year’s opening level of $1.35.
"In spite of the possibility of some political stability being restored, the UK economy remains in a potentially dark place, and the FTSE 250 has served as a barometer with a drop of 26% this year.
"The FTSE 100, which has made a slight recovery to stand down by 5% in the year to date, opened cautiously positive in an important week for earnings. In particular, the banks showed some strength ahead of their reporting third quarter numbers which investors will scour for any further provisions in terms of bad debts, as well as slowdowns in both mortgage lending and investment banking (where applicable), as was seen in the recent updates from the US sector.
"In addition, updates from the likes of Shell (LON:RDSa), Unilever (LON:ULVR) and WPP (LON:WPP) will provide further colour to pockets of the economy which have had differing fortunes of late, given the strength of the oil price, the defensive protection of household products and muted advertising spending."
In equity markets, heavily-weighted miners were the worst performers, with Antofagasta (LON:ANTO), Rio Tinto (LON:RIO), Anglo American (LON:AAL) and Glencore (LON:GLEN) all weaker.
Asia-focused Prudential (LON:PRU) was the worst performer on the FTSE 100 following heavy losses in Asian markets.
On the upside, Auto Trader rallied after saying it had sold its Webzone subsidiary to Mediahuis Ireland for €30m.
Banks were also up ahead of third-quarter results this week, with Barclays (LON:BARC), Lloyds and NatWest (LON:NWG) all in the black.
Educational publisher Pearson (LON:PSON) advanced after reaffirming its expectations for full-year sales and adjusted operating profit as it posted a 7% jump in third-quarter underlying sales.
Asos surged following a report over the weekend that Frasers Group has built a 5% stake in the online fashion retailer and become its fourth-largest shareholder.
Market Movers
FTSE 100 (UKX) 6,952.54 -0.25%
FTSE 250 (MCX) 17,285.87 0.46%
techMARK (TASX) 4,133.05 0.23%
FTSE 100 - Risers
Persimmon (LON:PSN) 1,255.00p 3.00%
Auto Trader Group (AUTO) 499.20p 2.67%
Pearson (PSON) 910.60p 2.61%
Next (NXT) 4,843.00p 2.22%
SSE (LON:SSE) 1,480.50p 2.10%
Taylor Wimpey (LON:TW.) 90.26p 1.87%
NATWEST GROUP (NWG) 239.40p 1.83%
Lloyds Banking Group (LON:LLOY) 42.14p 1.82%
Berkeley Group Holdings (The) (BKG) 3,366.00p 1.81%
Bunzl (LON:BNZL) 2,736.00p 1.56%
FTSE 100 - Fallers
Prudential (PRU) 835.60p -5.73%
Antofagasta (ANTO) 1,114.00p -2.96%
Shell (SHEL) 2,282.50p -2.62%
Rio Tinto (RIO) 4,699.50p -2.20%
Anglo American (AAL) 2,675.00p -2.16%
Standard Chartered (LON:STAN) 554.80p -2.15%
Ocado Group (LON:OCDO) 474.90p -2.00%
Glencore (GLEN) 493.60p -1.69%
Harbour Energy (HBR) 368.70p -1.47%
Scottish Mortgage Inv Trust (SMT) 740.20p -1.07%
FTSE 250 - Risers
Indivior (INDV) 1,539.00p 5.77%
Bank of Georgia Group (BGEO) 2,110.00p 4.20%
ASOS (LON:ASOS) (ASC) 530.00p 3.92%
Kainos Group (KNOS) 1,260.00p 3.28%
Jlen Environmental Assets Group Limited NPV (JLEN) 121.00p 3.24%
Redrow (LON:RDW) 414.00p 3.04%
Bridgepoint Group (Reg S) (BPT) 198.20p 2.85%
Supermarket Income Reit (SUPR) 99.80p 2.46%
AJ Bell (AJB) 300.40p 2.39%
Dunelm Group (LON:DNLM) 799.00p 2.24%
FTSE 250 - Fallers
Jupiter Fund Management (JUP) 93.65p -6.26%
Fidelity China Special Situations (LON:FCSS) 194.00p -6.05%
Ferrexpo (FXPO) 112.10p -5.16%
Abrdn Private Equity Opportunities Trust (APEO) 389.00p -2.99%
Darktrace (LON:DARK) 338.00p -2.85%
Schroder Oriental Income Fund Ltd. (SOI) 234.50p -2.70%
Sirius Real Estate Ltd. (SRE) 67.40p -2.60%
Dr. Martens (DOCS) 217.80p -2.51%
Synthomer (SYNT) 100.60p -2.33%
JPMorgan (NYSE:JPM) Emerging Markets Inv Trust (JMG) 95.10p -2.06%